# Math - equation of plane and vectors

163,269 results

### Math - equation of plane and vectors

A plane is defined by the equations x-4y+2z=16. Find two vectors parallel to the plane.

### Math - equation of plane and vectors

A plane is defined by the equations x-4y+2z=16. Find two vectors parallel to the plane.

### Math - Equations of plane(check)

Consider the plane that contains points A(2,3,1), B(-11,1,2), C(-7,-3,-6). a) Find two vectors that are parallel to the plane. Ans: AC, BC or AB will be parallel to the plane. b) Find two vectors that are perpendicular to the plane. Ans: if i find the normal vector then i can ...

### Math - Equations of plane(check)

Consider the plane that contains points A(2,3,1), B(-11,1,2), C(-7,-3,-6). a) Find two vectors that are parallel to the plane. Ans: AC, BC or AB will be parallel to the plane. b) Find two vectors that are perpendicular to the plane. Ans: if i find the normal vector then i can ...

### Maths - Vectors

The position vectors a,b,c of the points A,B,C relative to the origin O are ai, bj and ck respectively.Find: 1) a vector equation for the line l throught O which is normal to the plane ABC. 2) a vector equation of the plane ABC The answers should be: 1) r=t(bc i +ac j +ab k) ...

### Math

Me, again... Please help me. Thank you. Assume a plane is flying directly north at 200 mph, but there is a wind blowing west at 23 mph. Part I: Express both the velocity of the plane and the velocity of the wind as vectors, using proper notation to represent each direction of ...

### Calculus and vectors

Verify please and thank you~ 1. Does the line (x-7)/3=(y+8)/6=(z+4)/5 and the point P(10,-2,1) determine a plane? Answer: Yes, it is a plane because when I substituted the point P(10,-2,1) into the equation, I got the coordinates (1,1,1) If the coordinate became to be (0,0,0) ...

### math

Hi, I was working on my math homework and I was stumbling on these problems. I tried looking at the solutions but my answers were completely off. Here are the ones I'm stuck on: If vectors O(0,0,0), A(6,0,0), B(6,-sqrt(24), sqrt(12)), and C(0,-sqrt(24), sqrt(12)) form a square...

### vectors HELP!

determine an equation of the plane that is perpendicular to the plane x+2y+4=0, contains the origin, and has a normal that makes an angel of 30 degrees with the z-axis.

### Math - Vectors

Let the points A = (−1, −2, 0), B = (−2, 0, −1), C = (0, −1, −1) be the vertices of a triangle. (a) Write down the vectors u=AB (vector), v=BC(vector) and w=AC(vector) (b) Find a vector n that is orthogonal to both u and v. (c) Find a ...

### Calculus and vectors

A plane, π, has 3x-5z+3=0 as its Cartesian equation. Determine the Cartesian equation of a plane that is perpendicular to π and contains the point P(2,9,-3)

### VECTORS

Write a scalar equation of each plane, given its vector equation. [x,y,z] = [3,7,-5] + s[1,2,-1] + t[1,-2,3]

### vectors

find the vector form of the equation of the line in lR^3 that passes through P=(-1,0,3) and is perpendicular to the plane with a general equation x-3y+2z = 5

### vectors

What is the cartesian equation of the xz plane

### Math

Suppose that a wind is blowing in the direction S45°E at a speed of 50 km/h. A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 150 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors ...

### Vectors

Find the equation of the plane equidistant from the points (2,8,3) and (4,12,9)

### 12th grade

prove that normal to plane containing 3 points whose position vectors are a vector,b vector,c vectorlies in direction addition of cross product of vectors b and c and cross product of vectors c and a and cross product of vectors a and b

### vectors

If two vectors u and v fit the equation (u − v) • (u − v) = u•u+v•v, how must these vectors u and v be related? What familiar theorem does this equation represent?

### Calculus and vectors

Do the vectors (2,0,1),(-2,0,0) and (2,3,0) lie on the same plane? Explain your reasoning.

### Vectors

Given vectors A = -4.8i + 6.8j and B = 9.6i + 6.7j, determine the vector C that lies in the xy plane perpendicular to B and whose dot product with A is 20.0.

### Vectors

L1: [x,y,z] = [1,-2,4,] + s[1,1-3] L2: [x,y,z] = [4,-2,k] + t[2,3,1] Determine a value of k that is 10 units away from the plane with the equation 10x-7y+Z-28=0

### math

Hi I need help with this math problem: The plane that contains the points (8,3,1), (2,6,3), and (4,6,2) has an equation of the form ax + by + cz = d. Find coefficients for this equation, trying two different approaches to the problem. One method uses vectors, another does not...

### math

Hi, I was working on my math homework and I was stumbling on these problems. I wanted to double check my answers that I have; I also could not answer 5. If vectors O(0,0,0), A(6,0,0), B(6,-sqrt(24), sqrt(12)), and C(0,-sqrt(24), sqrt(12)) form a square. 1) Find a vector ...

### Geometry & Vectors

find an equation for the plane passing through the points Pi(3,1-2), Pii(-1,2,4) and Piii(2,-1,1)

### Vectors

Consider the lines L1: [x,y,z] = [4,-2,k] + s[1,1-3] +t[2,3,1] Determine a value of k that is 10 units away from the plane with the equation 10x-7y+Z-28=0

### math

given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the dot product of vectors p and q?

### Physics

2. We have two vectors that line in the x-y plane. If we take the cross-product of those two vectors we know that a. the magnitude of the cross-product will always be equal to the product of the magnitudes of the two vectors. b. the magnitude of the cross-product will always ...

### math

given that vectors(p+2q) and (5p-4q) are orthogonal,if vectors p and q are the unit vectors,find the product of vectors p and q?

### Math Vectors

A plane is heading on a bearing of 200° with an air speed of 400 km/h when it is blown off course by a wind of 100 km/h from the northeast. Determine the resultant ground velocity of the plane. How did you get your answer?

### physics

A novice pilot sets a plane's controls, thinking the plane will fly at 2.50 * 2 to the 2nd power km/h to the north. if the wind blows at 75km/h toward the southeast, what will the plane's new resultant velocity be? use graphical techniques. Are you sure you don't mean the ...

### math: Calculus - Algebraic Vectors

A light plane is travelling at 175 km/h on a bearing of N8°E in a 40 km/h wind from N80°E. Determine the plane's ground velocity using algebraic vectors. The answer for this question is: 167 km/h , N5°W ---------------- My Work: (a , b) = ( | r | * cosθ , | r | * sin&#...

### Physics - Vectors/Forces

A 10 kg weight is on an inclined plane 10 ft long and 6 ft high. If there is no friction, what force parallel to the plane will prevent the body from sliding?

### Vectors

Determine the vector equation of a plane that contains the line with symmetric equation (x+3)/-2=(y+1)/5=(z+2)/4 and the point P(1,3,0). For this question to find the direction vector you would use subtraction with the points (-3,-1,-2) and (1,3,0). Why would it be (1,3,0)-(-3...

### math

Given the plane 2x-3y+7z=4, a) Find the equation for the line perpendicular to the plane that intersects the plane at the point P=(6,5,1). b) How far is it from the point (4,-2,3) to the plane?

### vector

If two vectors u and v fit the equation (u − v) • (u − v) = u•u+v•v, how must these vectors u and v be related? What familiar theorem does this equation represent?

### Math

Given the plane 2x-3y+7z=4, find the equation for the line perpendicular to the plane that intersects the plane at the point (6,5,1).

### Math - Algebraic Vectors

Given the vectors: u = [3, 0] v = [-1, 2] a) Express the vector w = [2, 8] as a linear combination of vectors u and v. How do I do this?

### math

two vectors are defined as a=2i+xj and b=i-4j. find value of x if a) the vectors are parallel b) the vectors are perpendicular

### math

two vectors are defined as a=2i+xj and b=i-4j. find value of x if a) the vectors are parallel b) the vectors are perpendicular

### Vectors

How did you get your answer? A plane is heading on a bearing of 200° with an air speed of 400 km/h when it is blown off course by a wind of 100 km/h from the northeast. Determine the resultant ground velocity of the plane.

### math

if vectors a+b+c=0 and modulus of the vectors a, b and c are 3 ,5 and 7 respectively. find the angle between the vectors a and b.

### physics [vectors]

The concept i get, but somehow i just can't execute this problem, please help me! You are given vectors A = 5.5 6.2 and B = - 3.7 7.4 . A third vector C lies in the xy-plane. Vector C is perpendicular to vector A and the scalar product of C with B is 19.0. I need x and y ...

### Calculus and Vectors

A plane is flying south east at a constant speed of 900km/h. The wind is blowing towards the north at 100km/h. Determine the resultant velocity of the plane relative to the ground.

### Calculus

Sketch the vector field F⃗ (r⃗ )=2r⃗ in the plane, where r⃗ =⟨x,y⟩. Select all that apply. A.All the vectors point away from the origin. B. The vectors increase in length as you move away from the origin. C. All the vectors point toward ...

### physics

Suppose vector A=3i-2j, B= -i-4j and vector C are three vectors in xy plane with the property that vectors A+B-C. What is the unit vector along vector C?

### Math

Let a, b, and c be unit vectors, such that a+b+c=0. Show that the angle between any two of these vectors is 120 degrees. I proved this geometrically, but now my teacher wants a proof using vectors, and I don't know what to do.

### physics: scalars/vectors

Please check. 1. Which of the following quantities are scalars, and which are vectors? a. the acceleration of a plane as it takes off- VECTOR b. the number of passengers on the plane- SCALAR c. the duration of the flight- SCALAR d. the displacement of the flight- VECTOR e. the...

### 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) ...

### Calculus

Find the scalar equation of the plane through the points M(1,2,3) and N(3,2,-1) that is perpendicular to the plane with equation 3x + 2y + 6z +1 = 0. I know that normal of the latter equation is (3,2,6) but now what do I do? Thanks.

### Vectors

Show that the line with parametric equations x = 6 + 8t, y = −5 + t, z = 2 + 3t does not intersect the plane with equation 2x − y − 5z − 2 = 0.

### math

Find the unit vector perpendicular to the plane ABC where the position vectors of A, B and C are 2 ^i – ^j + ^ k , ^i + ^j + 2 ^ k and 2 ^i + 3 ^ k respectively.

### Physics

A 42-kg box slides down a frictionless inclined plane. The angle of the inclined plane is 34.0 degrees. The distance from the box to the bottom of the inclined plane is 3 m. Draw the free body diagram of the force vectors acting on the box. Determine: a. The weight of the box ...

### Vectors

3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the cartesian equation for the plane @ parallel to $ and containing the point (1,1,2) (ii)Calculate the distance between $ and @ (b)(i)Find the parametric equations for the line of intersection of the planes $ ...

### vectors

3 planes; $: x+2y-2z-6=0 %: 2x-y+z+8=0 £: 2x-y+2z+3=0 (a)(i)Find the cartesian equation for the plane @ parallel to $ and containing the point (1,1,2) (ii)Calculate the distance between $ and @ (b)(i)Find the parametric equations for the line of intersection of the planes $ ...

### Physics

Please help me with this its very hard to visualize the problem. The analytical method of adding vectors expressed in terms of their components may be applied to vectors in three dimensions, for which graphical work is inconvenient. Find the magnitude of the resultant of the ...

### maths

1) Suppose that an insect crawls in a plane in a path given in polar coordinates by r = be^kt; theta = kt; where b; k are positive constants and t is time.Find the velocity and acceleration vectors of the insect. Show that the angle between the velocity and acceleration ...

### Math:Calculus

Determine vector and parametric equations for the plane containing the point P0(1, -2, 3) and having direction vectors a= (4, -2, 5) and b = (-3, 3, 7). Thanks for the help.

### Math

The plane P1 has equation r = (2,1,1)+lambda(-2,1,8)+mu(1,-3,-9) The plane P2 has equation r = (2,0,1)+s(1,2,1)+t(1,1,1) Show that for points that lie on P1 and P2, lambda=mu I have no idea how to start... help! Thanks!

### Math

The altitude of a plane as it begins to descend is shown by the linear equation a = 22,000 – 800m, where a is the plane’s altitude, in feet, and m is minutes. What is the plane’s altitude when m = 12? ft

### Math- intersection of planes

Show that the line [x,y,z]=[10,5,16]+t[3,1,5] is contained in the plane x+2y-z-4=0 I tries writing the vector equation in parametric form and then substituting it into the respective x,y,z in the plane, after simplifying I get 0t=0 does this mean that the line is in the plane ...

### Trig

This has to do with vectors...I'm wondering if I set up the diagram correctly? A plane has a speed of 250mph and flies with a bearing of N35degE. The wind is blowing from the west at 25 mph with a heading of due east. What is the actual speed and heading of the plane?

### calc 3

The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45°W at a speed of 40 km/h. (This means that the direction from which the wind blows is 45° west of the northerly direction.) A pilot is steering a plane in the direction ...

### Physics - Torque

A particle is acted on by two torques about the origin: T1 has a magnitude of 4.3 N*m and is directed in the positive direction of the x axis, and T2 has a magnitude of 3.2 N*m and is directed in the negative direction of the y axis. What are the magnitude [in N*m] and ...

### 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?

### PreCalculus

Given vectors u=7i + 3j and v = -4i + 3j, find 5u-4v in terms of unit vectors. I am just beginning the study of vectors and have this problem. Could someone help? Thanks.

### Math

A commuter plane flies from City A to City B, a distance of 90 mi due north. Due to bad weather, the plane is redirected at take-off to a heading N 60° W (60° west of north). After flying 57 mi, the plane is directed to turn northeast and fly directly toward City B. To the ...

### Math

Find an equation of a plane through the point (2, -1, 0) which is parallel to the plane -1x-2y+4z=7.

### Calculus 3

Find the equation of the plane that passes through (1,0,0) and is perpendicular to the line r=<1,0,2>+t<1,0,1>. The vector equation of a plane is n*(r-rsub0)=0. Thank you so much for your help!

### Vectors

Determine a vector that is parallel to the plane: x + 2y + 2z - 5 = 0

### vectors

find three points on each plane [x,y,z]= [3,4,-1]+s[1,1,-4]+ t[2,-5,3]

### math

If A^TA is an invertible matrix, prove that the column vectors of A are linearly independent. You know that if statement X implies statement Y then that is equivalent to Not(Y) implies Not(X). You can start by taking the column vectors of to be linearly dependent and then show...

### Calculus

Name two sets of vectors that could be used to span a set in R^3. Show how the vectors (-1,2,0) and (3,4,0) could each be written as a linear combination of the vectors you have chosen.

### 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?

### Math & a bit of Physics

A block of mass 11 kg is at rest on a rough plane inclined at 30° to the horizontal. A force acts on the block in a direction up the plane parallel to a line of greatest slope. When the magnitude of the force is 2X N the block is on the point of sliding down the plane, and ...

### math

sketch the plane x+2y-z=6. if you need help,find a third line by letting z=0 and then graph the resulting equation in the xy plane

### math

Hi I wanted to check my work for this problem. Consider the points A(1,0,0) B(2,2,2) and C(0,2,1). 1) Find the vector CA x CB I got -2i -3j +4k for this 2) Find an exact value for the area of the triangle ABC. I got sqrt29/2 for this. 3) Plane II(1) is 2x+3y-4z=2. A second ...

### Calculus

Show that the vectors (-1,2,3), (4,1,-2) and (-14,-1,16) do not lie on the same plane

### Math- Intesection of a plane and line

Does the line [x,y,z]=[5,-9,3]+k[1,-12,2] intersect the plane [x,y,z]=[4,-15,8]+s[1,-3,1]+t[2,3,1]? If so, how many solutions are there? ( I tried finding the normal vector, there after finding the "d" value to write in scalar equation, and once it is in scalar equation i ...

### Calculus and Vectors

THE VECTORS a - 5b AND a-b ARE PERPENDICULAR. IF a AND b ARE UNIT VECTORS, THEN DETERMINE a dot b

### Physics

1. Consider the two vectors P and Q. The definition of P is P = i × (i × j). The definition of Q is Q = (i × i) × j . a. The magnitude of P is equal to the magnitude of Q. b. The magnitude of P is greater than the...

### physics

Two planes are initially separated by a horizontal distance of 350 km. Plane A is positioned 350 km west of the Plane B. Plane A is initially traveling at a velocity of 60 m/s east. Plane B is traveling at a velocity of 45 m/s west. If plane A begins to accelerate east at a ...

### Math - vectors

For what value of t are these two vectors parallel? a) r = 4i + tj and s = 14i - 12j What I Know: vectors are parallel if one is a scalar multiple of the other. I need to find a way that r and s relate by finding what number you can multiply r by to equal s. What I Don't Know...

### vectors

Find the distance between the parallel line and plane: l: r=[2,0,1] + t[1,4,1] pi: 2x - y + 2z = 4

### Vector

4. A plane has Cartetiar equation 4x - 3y + 6z - 12 =-- 0. a. Determine vector and p.iramqtric conations for this plane. b. Determine the equation of a line that lies in the plane.

### trig

A plane is flying with an airspeed of 150 miles per hour and heading 155°. The wind currents are running at 25 miles per hour at 160° clockwise from due north. Use vectors to find the true course and ground speed of the plane.

### Calulas and VECTORS

THE VECTORS a - 5b AND a-b ARE PERPENDICULAR. IF a AND b ARE UNIT VECTORS, THEN DETERMINE a * b

### Vectors

Does the point of intersection between L1:(4,9,2)+s(1,-1,-1), seR and Ls: (2,11,4)+t(5,-3,-4), teR lie on the plane 3x-2y+3z+4=0?

### Calculus and vectors

Please, help I don't understand vectors T.T 1. In the prism, assume all dimensions have different lengths, state the following: a) state 3 equal vectors to DC⃗ b) state 4 opposite vectors to BC⃗ ------------------------------------- Here is the prism below, imgur ...

### vectors

Determine whether each statement is true or false. Provide a brief justification. a. Two lines with parallel direction vectors willnot intersect. b. Two linesthat are perpendicularin R3 willhave perpendicular direction vectors. c. Two linesthat havenon-paralleldirection ...

### Calculus grade 12

Explain why three directional vectors of the plane cannot me mutually perpendicular .

### Calculus grade 12

Explain why three directional vectors of the plane cannot me mutually perpendicular .

### Physics

A and B are vectors in the same plane. If A= 8i+6j. Find the vector B such that |A+B| = 14.14 units and A is perpendicular to B.

### Physics

A jet plane is flying at a constant altitude. At time t1=0 it has components of velocity Vx=90m/s, Vy=110m/s.At time t2=30.0s the components are Vx=-170m/s, Vy=40m/s.a).Sketch velocity vectors at t1 and t2.How do these two vectors differ?. For this time interval calculate b). ...

### Calculus

Verify please and thank you~ Does the line (x-7)/3=(y+8)/6=(z+4)/5 and the point P(10,-2,1) determine a plane? Answer: Yes, it is a plane because when I substituted the point P(10,-2,1) into the equation, I got the coordinates (1,1,1) If the coordinate became to be (0,0,0) ...

### Physics Vectors

two vectors A and B have magnitude such that A>B. We do not know the directions of the vectors. however we can say that the magnitude of the sum A+B must be between? a) B and 2A b)A and A+B c) A-B and A+B d) A-B and A e) B and A+B

### physical science

The resultant vector of two particular displacement vectors dose not equal the sum of the magnitudes of the individual vectors. Describe the directions of the two vectors.

### Physics

An air traffic controller observes two airplanes approaching the airport. The displacement from the control tower to plane 1 is given by the vector A , which has a magnitude of 220 km and points in a direction 32 degrees north of west. The displacement from the control tower ...

### Calculus and vectors

A parallelogram is formed by R^3 by the vectors PA=(3,2,-3) and PB=(4,1,5). The point P=(0,2,3). a) what are the location of the vertices? b) what are the vectors representing the diagonals? c) what are the length of the diagonals?

### Grade 12 Math

if a and b are unit vectors, and magnitude of vectors a +b = sq. root of 3, determine (2a-5b) dot (b+3a).