Question

What is the angle between `<6, 8 ,2 >` and `< -2, 7 ,-2 >`?

Answer 1

`58.7º`

Explanation:

I assume we are looking for the acute angle `theta`. If the question asks for the obtuse angle, just find `theta` and your answer will be `pi - theta`.

Every time we are looking for the acute angle between two direction vectors, we use the dot product:

`a*b=abs(a)abs(b) cos theta`
`6(–2) + 8(7) + 2(–2) = sqrt(6^2+8^2+2^2)sqrt((–2)^2+7^2+(–2)^2) cos theta`
`cos theta = 40/sqrt(5928)`
`theta = 58.699º ≈ 58.7º` (1dp)