If `|vec(a)| = sqrt(2) , |vec(b)| = 7` and ` vec(a) xx vec(b) = 2 hat(i) + 6 hat(j) + 3 hat(k)`. Find the angle between `vec(a)` and `vec(b)`.

Explanation

`|vec(a) xx vec(b)| = sqrt((2)^(2) + (6)^(2) + (3)^(2)) = sqrt(49) = 7`
`| vec(a) xx vec(b) | = ab sin theta = |vec(a)| |vec(b)| sin theta`
`sin theta = (|vec(a) xx vec(b)|)/(|vec(a)| |vec(b)|) = (7)/((sqrt(2)) (7)) = (1)/(sqrt(2)) rArr theta = 45^(@)`