Help with vectors, please. Thanks
1) Express point in rectangular form. Give EXACT answer, if possible?
(2, 4π /11)
2) Given P = (2. -3) and Q = (-3, -4). find the component form of vector PQ
3) The vector v has a magnitude of 25 inches and a direction of 32° , Express this vector in rectangular form.
perform each operation with vectors u = < 6, 2 > and v = < -10, 1 >
4) u+v 5) -3u
(x,y) = (2cos 4π/11,2sin 4π/11)
P = (√26,arctan(-1/-5))
v = 25cos32°i + 25cos32°j
u+v = <(6-10),(2+1)>
-3u = <-3(6),-3(2)>
Thanks.
For #3, I did not realize he gave me multiple choice answers.
A) (-13.25, 21.20)
B) (-21.20, -13.25)
C) (13.25, 21.20)
D) (21.20, 13.25)
I figured it out and think both have to be positive so the answer is D. Let me know if I'm wrong
Looks good to me.
Sure, I can help you with vectors. Let's go through each question one by one:
1) To express a point in rectangular form, you need to convert it from polar form. In this case, the point is given as (2, 4π/11).
To convert it to rectangular form, you can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
In this case, r = 2 and θ = 4π/11. Plugging these values into the formulas gives us:
x = 2 * cos(4π/11)
y = 2 * sin(4π/11)
To get the exact answer, you can leave it in this form. If you want a numerical approximation, you can use a calculator to evaluate the trigonometric functions.
2) To find the component form of vector PQ, you need to subtract the coordinates of point P from the coordinates of point Q. Given P = (2, -3) and Q = (-3, -4), the component form of vector PQ is:
PQ = (-3 - 2, -4 - (-3))
= (-5, -1)
So the component form of PQ is (-5, -1).
3) To express a vector with magnitude 25 inches and direction 32° in rectangular form, you can use the following formulas:
x = magnitude * cos(direction)
y = magnitude * sin(direction)
In this case, the magnitude is 25 inches and the direction is 32°. Plugging these values into the formulas gives us:
x = 25 * cos(32°)
y = 25 * sin(32°)
Performing the calculations will give you the rectangular form of the vector.
4) To perform vector addition (u + v), you simply add the corresponding components of the vectors. Given u = <6, 2> and v = <-10, 1>, the sum of u and v is:
u + v = <6 + (-10), 2 + 1>
= <-4, 3>
So u + v is equal to <-4, 3>.
5) To multiply a vector by a scalar (-3u), you simply multiply each component of the vector by the scalar. Given u = <6, 2>, multiplying u by -3 gives:
-3u = <-3 * 6, -3 * 2>
= <-18, -6>
So -3u is equal to <-18, -6>.
I hope this helps! Let me know if you have any further questions.