Vectors Question - For the vectors u=(2,-1,1) and v=(0,3,4)

Question

Find the following:

U•V

U x V

the angle between U and V to the nearest degree

Please include steps and answer

Answer 1

a) U•V = (2)(0) + (-1)(3) + (1)(4) = 1 [since this does not equal 0, not orthogonal]

b) U x V =

= (-4 - 3)i - (8 - 0)j + (6 - 0)k

= -7i - 8j + 6k

= <-7, -8, 6>

c) Find the angle between U and V to the nearest degree.

cosθ = (u·v)/|u||v|

u·v = 1 [from part a]

|u| = √((2)²+(-1)²+(1)²) = √6

|v| = √((0)²+(3)²+(4)²) = √25 = 5

cosθ = (u·v)/|u||v| = 1/5√6

Want the angle θ, so take the cos^-1 of both sides:

θ = cos^-1(1/5√6) = 60.66° ==> so the measure of the angle between u and v is about 60.7°.