Question

Prove that `|vec(a) xx vec(b)|=(vec(a)*vec(b)) tan theta," where " theta `is the angle between `vec(a) and vec(b)`.

Answer 1

`(vec(a) xx vec(b)) = |vec(a)| | vec(b)| sin theta * hat(n)`
`rArr | vec(a) xx vec(b)|=ab sin theta , " where " | vec(a)|=and |vec(b)|=b`
`=(ab cos theta) ( tan theta)=( vec(a)* vec(b)) tan theta.`