If `vec(a) = 2 hat(i) + 6 hat(j) + 3hat(k) , vec(b) = hat(i) + lambda hat(j) + mu hat(k)`. If `vec (a) xx vec(b) = 0` , find the value of `lambda` and `mu`.

Explanation

`vec(a) xx vec(b) = |(+ , - , +), (hat(i) , hat(j) , hat(k)) ,(2 , 6 , 3),(1 , lambda , mu)|`
`= hat(i) | ( 6 , 3) , (lambda , mu)| - hat(j)| (2,3),(1 , mu)| + hat(k) | (2 , 6),(1 , lambda)|`
` = hat(i) ( 6 mu - 3 lambda) - hat(j) ( 2 mu - 3) + hat(k) ( 2 lambda - 6) = 0`
` 2 mu - 3 = 0 rArr mu = (3)/(2)`
`2 lambda - 6 = 0 rArr lambda = 3`