Question

If `A = <5 ,4 ,8 >`, `B = <2 ,-7 ,6 >` and `C=A-B`, what is the angle between A and C?

Answer 1

`theta = arccos frac{75}{sqrt 14070}`

Explanation:

`C = ((3), (11), (2)), A = ((5), (4), (8))`

`A * C = |A| * |C| * cos theta`

`cos theta = frac{15+44+16}{sqrt{25+16+64} sqrt{9+121+4}}`

`cos theta = frac{75}{sqrt{3*5*7*2*67}}`