Question

If `A = <2 ,1 ,8 >`, `B = <5 ,2 ,3 >` and `C=A-B`, what is the angle between A and C?

Answer 1

`theta approx 47.82^circ`

Explanation:

`C=A-B=(2,1,8)-(5,2,3)=(-3, -1, 5)`

`A cdot C = |A| |C| cos theta`

`cos theta = {A cdot C}/{|A||C|} = {2(-3)+1(-1)+8(5)}/{sqrt{(2^2+1^2+8^2)(3^2+1^2+5^2)} }= 11 sqrt(3/805)`

`theta approx 47.82^circ`