Find the angle between vectors u = (1, -2, 4) and v = (-2, 0, 3) (when they are positioned tail to tail).

Question

1. Find the angle between vectors u (arrow on top) = (1, -2, 4) and v (arrow on top) = (-2, 0, 3) (when they are positioned tail to tail).

Answer 1

The scalar product between two vectors u and v is u.v =|u||v|cosθ where θ

is the angle between the vectors.

u.v=(1,-2,4).(-2,0,3)= 1(-2)+(-2)(0)+4(3)=-2+0+12=10

|u|=√21 and |v|=√13 so √(21.13)cosθ=10

θ=arccos(10/√(21.13))