Question

If `A = <7 ,-8 ,-2 >`, `B = <4 ,-8 ,8 >` and `C=A-B`, what is the angle between A and C?

Answer 1

`theta~~68.71^@`

Explanation:

`C=<7-4,-8--8,-2-8> = <3,0,-10>`

`cos theta = (A*C)/(|A| |C|)`

`cos theta=(<7,-8,-2>*<3,0,-10>)/((sqrt(7^2+(-8)^2+(-2)^2))(sqrt(3^2+0^2+(-10)^2)))`

`cos theta=(21+0+20)/(sqrt117sqrt109) = 41/sqrt12753`

`theta=cos^-1 (41/sqrt12753)`

`theta~~68.71^@`