# the magnitude of 2 vectors are 4 and 5 units and the angle b/w them is 30,taking first vectoron x-axis.find the magnitudeof resultant vectorand its direction?

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### physics

the magnitude of 2 vectors are 4 and 5 units and the angle b/w them is 30,taking first vectoron x-axis.find the magnitudeof resultant vectorand its direction?

### physics

The magnitude of vector A is 18 units at an angle of 90 degrees with the x-axis, and the magnitude of vector B is 12 units at an angle of 330 degrees with the x-axis. What vector C must be added to the vectors A and B so that the resultant of these three vectors points in the ...

### Physics

A. Given two vectors ~F1, and ~F2. Where the magnitude of these vectors are F1= 81 N, and F2= 90 N. And where θ1= 80◦,and θ2= 22◦. The angles are measure from the positive x axis with the counterclockwise angular direction as positive. What is the ...

### Physics

The magnitudes of the four displacement vectors shown in the drawing are A = 14.0 m, B = 11.0 m, C = 12.0 m, and D = 25.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs when these vectors are added together. Specify the direction as a positive (...

### physics

Three vectors are shown in Fig. 3-32 (A = 62.0 , B = 58.0°). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. (a) Give the resultant in terms of components. Rx = Ry = (b) What is the magnitude of the resultant? What is the resultant's ...

### physics

Three vectors are shown in Fig. 3-32 (A = 60.0 , B = 56.0°). Their magnitudes are given in arbitrary units. Determine the sum of the three vectors. (a) Give the resultant in terms of components. (b) What is the magnitude of the resultant? What is the resultant's angle above ...

### physics

Find the resultant, in magnitude and direction of a force of 40 N which makes an angle with the + X axis of 38o and a force of 20 N acting along the + X axis. Find the x and y components of the resultant and express them as i and j vectors.

### Physics

1) The vector sum of three vectors gives a resultant equal to zero. what can you say about the vectors? 2) Vector is 3.00 units in length and points along the positive x-axis. Vector is 4.00 units in length and points along the negative y-axis.Use graphical methods to find the...

### Science

1) The vector sum of three vectors gives a resultant equal to zero. what can you say about the vectors? 2) Vector is 3.00 units in length and points along the positive x-axis. Vector is 4.00 units in length and points along the negative y-axis.Use graphical methods to find the...

### Physics

Find the magnitude and direction of the resultant R of the three vectors shown in figure 1.3. The vectors have the following magnitudes: A=5.0, B=7.9, and C=8.0. Express the direction of the vector sum by specifying the angle it makes with the positive x-axis, with the ...

### Physics

Consider three force vectors ~ F1, ~ F2, and ~ F3 with magnitude 43 N and direction 53; mag- nitude 94 N and direction 162; and magni- tude 59 N and direction 288, respectively. All direction angles are measured from the posi- tive x axis: counter-clockwise for > 0 and...

### Physics

Consider three force vectors ~ F1, ~ F2, and ~ F3. The vector ~ F1 has magnitude F1 = 86 N and direction θ1 = 169◦; the vector ~ F2 has magni- tude F2 = 46 N and direction θ2 = 240◦; and the vector ~ F3 has magnitude F3 = 45 N and direction θ3 = 132...

### Physics

The three displacement vectors have a magnitudes of a= 5.00 meters, b= 5.00 meters, and c= 4.00 meters. Find the resultant magnitude and Direction angle of the three vectors by names of the component method. Express the directional angle as an angle above the positive or ...

### Physics

Vector has a magnitude of 8.10 units and makes an angle of 52.0° with the positive x-axis. Vector also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods find the following. a) The vector sum Magnitude of A + B:___ units Direction...

### Physics

Vectors A and B are in the xy plane and their scalar product is 20.6 units.? If A makes a 27.8 angle with the x axis and has magnitude A= 14.8 units, and B has magnitude B= 29.0 units, what can you say about the direction of B?

### Physics

Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 16.0 m, B = 12.0 m, C = 13.0 m, and D = 23.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs ...

### physics

Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 15.0 m, B = 10.0 m, C = 12.0 m, and D = 29.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs ...

### physics

Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 17.0 m, B = 10.0 m, C = 11.0 m, and D = 23.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs ...

### science

vector A has a magnitude of 12 units and makes an angle of 30 with the positive x-axis.vector b has a magnitude of 8 units and makes an angle of 80 with the positive x-axis.using a graphical method , find the magnitude and direction of vectors A-B

### physics

Four forces are acting on an object. Force 1 has a magnitude of 5N at an angle of 70° above the +x-axis; force 2 has a magnitude of 8N at an angle of 35° above the +x-axis; force 3 has a magnitude of 4N at an angle of 20° above the -x-axis; force 4 has a magnitude of 7N at ...

### Elementary mechanics

(Q1) 2 forces act on a point object as follows: 100 at 170 and 100 at 50.Find the resultant force (a)110N at 50 (b)110N at 100 (c)100N at 110 (d) 100N at 50 (Q2) given 3 vectors a=-i-4j+2k,b=3i+2j-2k,c=2i-3j+k,Calculate a-(b-c) (a)-6(b)6(d)9(d)-9 (Q3)The resultant of vectors A...

### Physics

A force F 1 of magnitude 5.90 units acts on an object at the origin in a direction θ = 28.0° above the positive x-axis. (See the figure below.) A second force F 2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the ...

### Physics

A force F1 of magnitude 6.90 units acts on an object at the origin in a direction θ = 54.0° above the positive x-axis. (See the figure below.) A second force F2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the ...

### physical

three displacement vectors of a croquet ball are shown in figure p3.49, where |a| = 20.0 units, |b| = 40.0 units, and |c| = 30.0 units. find (a) the resultant in unit–vector notation and (b) the magnitude and direction of the resultant displacement

### physics

A force Farrowbold1 of magnitude 5.00 units acts on an object at the origin in a direction θ = 34.0° above the positive x-axis. (See the figure below.) A second force Farrowbold2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find ...

### physics

A particle undergoes two displacements. The first has a magnitude of 160 cm and makes an angle of 105.0° with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35.0° to the positive x axis. Find the magnitude and ...

### physics

A particle undergoes two displacements. The first has a magnitude of 135cm and makes an angle of 114° with the positive x axis. The resultant displacement had a magnitude of 183cm and is directed at an angle of 21.8° to the positive x axis. Find the magnitude of the second ...

### science

Find the resultant of vectors angle A of magnitude 10units in the direction N40E and angle B of magnitude 8units in the direction S30E.

### chemistry

A man pushing a mop across a floor causes it to undergo two displacements. The first has a magnitude of 152 cm and makes an angle of 125° with the positive x axis. The resultant displacement has a magnitude of 150 cm and is directed at an angle of 35.0° to the positive x ...

### college physics

A man pushing a mop across a floor causes it to undergo two displacements. The first has a magnitude of 140 cm and makes an angle of 130° with the positive x axis. The resultant displacement has a magnitude of 144 cm and is directed at an angle of 30.0° to the positive x ...

### physics

A man pushing a mop across a floor causes the map to undergo two displacements. The first has a magnitude of 200 cm and makes an angle of 120° with the positive x axis. The resultant displacement has a magnitude of 240 cm and is directed at an angle of 60.0° to the positive ...

### physics

Can anyone help just can figure it out. Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 17.0 m, B = 10.0 m, C = 11.0 m, and D = 23.0 m. Determine the (a) magnitude and (b) ...

### physics

Vector vector A has a magnitude of 6.90 units and makes an angle of 46.5° with the positive x-axis. Vector vector B also has a magnitude of 8.00 units and is directed along the negative x-axis. Using graphical methods find the following. (a) The vector sum vector A + vector B...

### Physics

1. Consider four vectors ~F1, ~F2, ~F3, and ~F4, where their magnitudes are F1= 57 N, F2= 38 N, F3= 25 N, and F4= 67 N. Let θ1= 130◦, θ2=−130◦, θ3= 29◦, and θ4=−64◦, measured from the positive x axis with the counter-...

### physics

Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 17.0 m, B = 10.0 m, C = 11.0 m, and D = 23.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs ...

### Physics

A football player runs the pattern given in the drawing by the three displacement vectors A, B, and C. The magnitudes of these vectors are A = 5 m, B = 13.0 m, and C = 16.0 m. Using the component method, find the magnitude and direction è of the resultant vector A + B + C. (...

### Trig

I need help setting these up. 1.) Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in the figure. round to one decimal place. Theta= 35 degree, b=98 lbs, c=55lb 2.) Find the magnitude and direction angle for each vector. Five the...

### physics

Two vectors of magnitudes 10 units and 15 units are acting at a point. The magnitude of their resultant is 20 units. Find the angle between them.

### Physics

a) You have two forces, 105.5 N and 61.5 N. What is the magnitude of their resultant if the first acts upward and the second acts downward? Answer in units of N. b) What is the direction of the resultant? c) What is the magnitude of their resultant if they both act downward? ...

### physics

Three displacement vectors of a croquet ball are shown in figure below, where |A| = 20.0 units, |B| = 40.0 units, and |C| = 30.0 units. Calculate (a) the resultant in unit-vector notation and (b) the magnitude and direction of the resultant displacement

### physics

Can you help me with this one also? I know how to do it with 3 vectors but I can't seem to draw it with 4 vectors. The magnitudes of the four displacement vectors shown in the drawing are A=16.0 m, B=11.0 m, C=12.0 m, and D=26.0 m. Determine the (1) magnitude and (2) ...

### College Physics

14) Given the following vectors, find the magnitude and direction: • A = 47 m and the angle is 0° • B = 62 m and the angle is 35° This is relative to the x-axis Magnitude: 401 m 140 m 104 m 0 m 503 m Direction: 20° 45° 55° 220° 90°

### Physics

A force 1 of magnitude 7.20 units acts on an object at the origin in a direction θ = 29.0° above the positive x-axis. (See the figure below.) A second force 2 of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the ...

### Physics

Four forces are acting on an object. Force 1 has a magnitude of 5N at an angle of 70° above the +x-axis; force 2 has a magnitude of 8N at an angle of 35° above the +x-axis; force 3 has a magnitude of 4N at an angle of 20° above the -x-axis; force 4 has a magnitude of 7N at ...

### physics

The three displacement vectors in the drawing have magnitudes of A = 5.73 m, B = 6.48 m, and C = 3.12 m. Find the resultant ((a) magnitude and (b) directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the ...

### Physics

The three displacement vectors in the drawing have magnitudes of A = 5.48 m, B = 5.23 m, and C = 4.75 m. Find the resultant ((a) magnitude and (b) directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the ...

### math

Two vectors have magnitudes of 3 units and 8 units respectively. The resultant of these two vectors has a magnitude of 8 units. What is the angle between these two vectors?

### physics

A football player runs the pattern given in the drawing by the three displacement vectors A, B, and C . The magnitudes of these vectors are A = 5 m, B = 16.0 m, and C = 16.0 m. Using the component method, find the magnitude and direction è of the resultant vector A,B,C. (...

### Physics

A vector has magnitude 58.0 units and is inclined to the positive axis of x at 42.0°. Vector has magnitude 36.0 units and is inclined to the positive axis of x at 121°. Vector has magnitude 40.0 units and is inclined to the positive axis of x at 53.0°. Use the graphical ...

### Discrete Math - Vectors

Can you please help me correct my answers for the following two questions? 1) A tour boat travels 25 km due east and then 15 km S50°E. Represent these displacements in a vector diagram, then calculate the resultant displacement. ====== My Work: I drew the vectors and ...

### Physics

Vector Aarrowbold points in the negative y direction and has a magnitude of 8 units. Vector Barrowbold has the same the magnitude and points in the positive x direction. Find the direction and magnitude of the following vectors. a) Aarrowbold + Barrowbold magnitude direction...

### Vectors

I hope that the diagram I have drawn for myself matches the one in your question. I have a triangle with sides 20 and 10 and an angle of 120º between them By the cosine law I found the third side to be 26.4575. You said you found the maginitude, I hope we match. After that, ...

### Physcis(Please help)

A pilot flies her route in two straight-line segments. The displacement vector A for the first segment has a magnitude of 254 km and a direction 30.0o north of east. The displacement vector for the second segment has a magnitude of 178 km and a direction due west. The ...

### Physics

A golfer, putting on a green requires three strokes to “hole the ball.” During the first putt, the ball roles 5.0m due east. For the second putt, the ball travels 2.1m at an angle of 20 degrees north of east. The third putt is 0.50m due north. What displacement (magnitude ...

### Physics

A golfer, putting on a green requires three strokes to “hole the ball.” During the first putt, the ball roles 5.0m due east. For the second putt, the ball travels 2.1m at an angle of 20 degrees north of east. The third putt is 0.50m due north. What displacement (magnitude ...

### phy111

The resultant of vectors A and B has a magnitude of 20 units.A has a magnitude of 8 units, and the angle between A and B is 40o. Calculate the magnitude of B

### PHYSICS

Vector A⃗ points in the negative x direction and has a magnitude of 22 units. The vector B⃗ points in the positive y direction. partA:Find the magnitude of B⃗ if A⃗ +B⃗ has a magnitude of 37 units. partB: Sketch A⃗ and B⃗ . Draw the vectors with their tails at ...

### Physics

Given Vector A with magintude 9.17 feet and Vector B with magnitude of 10.58 feet, what is the resultant of the two vectors added together? Answer: I know it would depend on the direction of the vector. If in the same line we would add them or if opposite lines we would ...

### Physics

2 displacement vectors of 15 meters and 10 meters are combined. a.Find the magnitude of the minimum possible resultant and the angle between the vectors. b. Find the magnitude of the maximum possible resultant and the angle between the vectors.

### Physics

Using a graphical method of getting resultant vectors, find the resultant of the following vectors: 8N along the positive X-axis and 6N making an angle of 45 degrees with the positive X-axis and 10N -20 degrees below West.

### Calc-Based Physics

Three Displacement Vectors of a Croquet Ball are shown, where A is 20.0 units at 90 degrees, B is 40.0 units at 45.0 degrees, and C is 30.0 at 315 degrees. Find: a) The resultant in unit-vector notation. AND b) The magnitude and direction of the resultant displacement. Sorry ...

### physics

A force 1 of magnitude 5.40 units acts at the origin in a direction 45.0° above the positive x axis. A second force 2 of magnitude 5.00 units acts at the origin in the direction of the positive y axis. Graphically find the magnitude and direction of the resultant force 1 + 2.

### Physics

A football player runs the pattern given in the drawing by the three displacement vectors , , and . The magnitudes of these vectors are A = 6.00 m, B = 13.0 m, and C = 15.0 m. Using the component method, find the (a) magnitude and (b)direction of the resultant vector + + . ...

### physics

A football player runs the pattern given in the drawing by the three displacement vectors , , and . The magnitudes of these vectors are A = 4.00 m, B = 15.0 m, and C = 18.0 m. Using the component method, find the (a) magnitude and (b)direction of the resultant vector + + . ...

### AP Physics

there are two vectors in quadrant three one with a magnitude of 31.0N and has a direction of 117degrees in the negative direction from the x axis the other has an unknown magnitude and unkown theta in the positive direction starting from 90 degrees Find the scalar product of ...

### Physics

Two point charges, q1 and q2, of 4.00 uc each, are placed -6.0 cm and 6.0 cm away from the origin on the x-axis. A charge q3 of -1.00 uC is placed 8.0 cm away from the origin on the y-axis. a. Find the distance from q3 to q1 and from q3 to q2. b, Find the magnitude and the ...

### Physics

Two point charges, q1 and q2, of 4.00 uc each, are placed -6.0 cm and 6.0 cm away from the origin on the x-axis. A charge q3 of -1.00 uC is placed 8.0 cm away from the origin on the y-axis. a. Find the distance from q3 to q1 and from q3 to q2. b, Find the magnitude and the ...

### Physics

Consider two vectors F~ 1 with magnitude 44 N inclined at 163 ◦ and F~ 2 with magnitude 72 N inclined at 236 ◦ , measured from the positive x axis with counterclockwise positive. What is the magnitude of the resultant vector F~ 1 + F~ 2 ? Draw the vectors to scale ...

### Physics

A football player runs the pattern given in the drawing by the three displacement vectors A ,B ,C and . The magnitudes of these vectors are A = 4.00 m, B = 17.0 m, and C = 19.0 m. Using the component method, find the (a) magnitude and (b)direction of the resultant vector A + B...

### Vectors

If /U/=9, /V/=11, and theta = 43 deg (angle between), find the magnitude of U+V and give the direction that the that the resultant makes with U.

### Physics

A particle undergoes two displacements, measured from the positive x-axis, with counterclockwise positive. The first has a magnitude of 11 m and makes an angle of 67 ◦ with the positive x axis. The resultant displacement has a magnitude of 7.7 m directed at an angle of ...

### DPS PHYCIS

LET A AND B BE THE TWO VECTORS OF MAGNITUDE 10UNITS EACH. IF THEY ARE INCLINED TO THE X-AXIS AT ANGLE 30` AND 60` FIND THE RESULTANT ALSO FIGURE

### Physics

What should be the angle between two vectors of magnitudes 3.20 and 5.70 units, so that their resultant has a magnitude of 6.10 units?

### Physics

What should be the angle between two vectors of magnitudes 4.10 and 4.40 units, so that their resultant has a magnitude of 3.90 units?

### Physics

three vectos are shown in fig. 3-32. their magnitudes are given in arbitrary units. Determine the sum of the three vectors. Give the resultant in terms of (a) components, (b) magnitude and angle with the x axis. (3-32 --the figure has three rays all starting at the origin. Ray...

### physics

Consider four vectors F1, F2, F3, and F4, with magnitudes are F1 = 41 N, F2 = 24 N, F3 =27 N, and F4 = 51 N, and angle 1 = 150 deg, angle 2 = −160 deg, angle 3 = 39 deg, and angle 4 = −57 deg, measured from the positive x axis with the counter clockwise angular ...

### Statics

If both the projection Pa and component Fb of the force F are 250 N, determine the magnitude of the resultant F and the orientation theta of the b-axis. There is a 34 degree angle from the resultant force to the a-axis. There is a 4 degree angle from the resultant force to the...

### science (physics) Need to solve this today please

(a) Express the vectors A, B, and C in the figure below in terms of unit vectors. (b) Use unit vector notation to find the vectors R = A + B + C and S = C – A – B. (c) What are the magnitude and directions of vectors R and S? Well the picture goes and has a vector A ...

### physics

find the resultant of vectors A of magnitude 10units in the direction N40E and B of magnitude 8units in the direction S30E

### Physics

I know I need to show my work but the problem is that I don't even know where to begin. I am taking an online physics class with a teacher that is not willing to help. So any guidance would be much appreciated. Consider the two vectors: F1: (220N, 41°), F2: (50N, 139°) The ...

### Physics

2 vectors have same magnitude.The magnitude of the resultant vector of these 2 vectors are same as either of both vectors.What is the angle between 2 vectors?

### Physics

What is the resultant of two displacement vectors having the same direction? a. The resultant is the sum of the two displacements having the same direction as the original vectors. b. The resultant is the difference of the two displacements having the same direction as the ...

### physics repost

What should be the angle between two vectors of magnitudes 3.20 and 5.70 units, so that their resultant has a magnitude of 6.10 units? cos=a^2+b^2-c^2/2ab cos10.24+32.49-37.21/(2*3.20*5.70) = 99 degrees

### Science

2 vectors have same magnitude.The magnitude of the resultant vectors is same as either of both vectors.What is the angle between 2 vectors?

### physics

Let A and B be the two vectors of magnitude 10 unit . If they are inclined to X-axis at angle 30 degree and 60 degree respectively. Find the resultant.

### physics

Vector A has magnitude 8.0 units at an angle of 60o from the x-axis. Vector B has magnitude 6.0 at an angle of -30o from the x-axis. Find the magnitude and direction of vector C = A + B I tried actually drawing it to see if it would help but it didn't I'm pretty sure the ...

### math

Find the Magnitude and direction of the resultant force. three forces with magnitude of 50,20, and 40 points acting on an object at angle 60 degres, 30 degrees, and -90degrees,k respectevly with the positive x-axis.

### physics

A particle undergoes two displaments , measured from the positive x-axis, with counterclockwise positive.The first has a magnitude of 11 m and makes an angle of 88 with the positive x-axis. The resultant displacement has a magnitude of 6.8 m direceted at an angle of 115 from ...

### geometry

1. Initial point: (0, 0); Terminal point: (3, -4) A Lesson 13 B Lesson 13 C Lesson 13 D Lesson 13 E Lesson 13 F Lesson 13 2. Initial point: (3, 5); Terminal point: (-2, -1) A Lesson 13 B Lesson 13 C Lesson 13 D Lesson 13 E Lesson 13 F Lesson 13 In problems 3 and 4, let u = ...

### physics

Consider three force vectors F1 with magnitude 42N and direction 140°, F2 with magnitude 27N and direction -110°, and F3 with magnitude 19N and direction 120°. All direction angles 0 (0 with a line inside) are measured from the positive x axis: counter-clockwise for 0 (with...

### Physics

A rocket lifts off its launching pas with a vertical velocity of 20. m/s and a horizontal velocity of 60. m/s. What are the magnitude and direction of its resultant velocity? I drew the x and Y axis. 20 m/s on the Y axis and 30 m/s on the X axis. I know I need to find the ...

### Physics

Two vectors F1 and F2 with magnitude F1=42N and F2=70N and where angle1=83 and angle2= 300. The angles are measures from the positive x axis with the counter-clockwise angular direction as positive. What is the magnitude of the resultant vector where F=F1+F2?

### Physics

A basketball player runs down the court, following the path indicated by the vectors A, B, and C in the figure. The magnitudes of these three vectors are: A = 12.0 m, B = 17.0 m, and C = 7.0 m. Let the +x-axis point to the right and the +y-axis point to the far side of the ...

### Physics

A man in search of his dog drives first 13.3 mi northeast, then 17.3 mi straight south, and finally 6.85 mi in a direction 30.3° north of west. 1. a) What is the magnitude of his resultant displacement? 2. b) What is the direction of his resultant displacement? Express your ...

### Physics

A man in search of his dog drives first 13.3 mi northeast, then 17.3 mi straight south, and finally 6.85 mi in a direction 30.3° north of west. a) What is the magnitude of his resultant displacement? b) What is the direction of his resultant displacement? Express your answer ...

### physics

1. A billiard ball of mass mA = 0.4 kg moving with a speed vA = 2 m/s strikes a second ball, initially at rest, of mass mB = 0.4 kg. As a result of the collision, the first ball is deflected off at an angle of 30.0o with a speed v’A = 1.2 m/s. Taking the xaxis to be the ...

### geometry

In problems 1 and 2, the initial point and the terminal point of a vector are given. Write the vector in component form. 1. Initial point: (0, 0); Terminal point: (3, -4) A Lesson 13 B Lesson 13 C Lesson 13 D Lesson 13 E Lesson 13 F Lesson 13 2. Initial point: (3, 5); Terminal...

### Vectors (Physics/Math)

Vector A has a magnitude of 18 (in some unspecified units) and makes an angle of 25 with the x axis, and a vector B has a length of 24 and makes an angle of 70 with the x axis. Find the components of the vector C in the following: (a) C = A + B Cx = Cy = (b) C = A - B Cx= Cy=

### Pysics science

The resultant of vectors A⃗ and B⃗ has a magnitude of 20 units. A⃗ has a magnitude of 8 units, and the angle between A⃗ and B⃗ is 40o . Calculate the magnitude of B⃗