Question

What is the angle between `<2,5,4 >` and `< 6,8,1 >`?

Answer 1

`33.83^@`

Explanation:

There are 2 methods we can use to calculate this algebraically, either using the vector cross product or the vector inner product.
I shall use the latter method as it is quicker and also more general.

The angle between any 2 vectors `A and B` in any dimensional vector space may be given by the inverse cosine of the Euclidean inner product of the 2 vectors divided by the product of the norms of the 2 vectors.
ie. `costheta=(A*B)/(||A||*||B||)`

`therefore theta=cos^(-1) (([(2,5,4) * (6,8,1)]) / (||((2,5,4))|| * ||((6,8,1))||))`

`=cos^(-1)((12+40+4)/(sqrt(45sqrt101)))`

`=33.83^@`.