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.