# Thread: vector componets

1. ## vector componets

Let u = 3i - 4j + 12k, and v = 2i + 2j - k

find 5u - 2v

find the length of u

find the length of v

find u * v

and find the angle between u and v. give your answer to the nearest 0.01

radians.

any help with these please.

2. Originally Posted by rcmango
Let u = 3i - 4j + 12k, and v = 2i + 2j - k

find 5u - 2v

find the length of u

find the length of v

find u * v

and find the angle between u and v. give your answer to the nearest 0.01

radians.

any help with these please.
u = 3i - 4j + 12k, and v = 2i + 2j - k

find 5u - 2v

<15, -20, 60> - <4, 4, -2> = <11, -24, 62>

find the length of u

sqrt(9 + 16 + 144) = sqrt(169) = 13

find the length of v

sqrt(4 + 4 + 1) = sqrt(9) = 3

find u * v (I'm assuming it is u dot v).

u.v = 6 + (-8) + (-12) = -14

find the angle between u and v. give your answer to the nearest 0.01

radians.

u.v/||u||||v|| = cos(theta)

-14/(13*3) = cos(theta)

-14/39 = cos(theta)

arccos(-14/39) = theta

And thus, the angle is: 1.94 radians.