If `vec(a)=(2hat(i)+6hat(j)+27hat(k)) and vec(b)=(hat(i)+lambda(j)+mu hat(k))` are such that `vec(a)xxvec(b)=vec(0)` then find the values of `lambda` and`mu`.

Answer

`lambda=3, mu=(27)/(2)`

Explanation

`(vec(a)xxvec(b))=|(hat(i),hat(j),hat(k)),(2,6,27),(1,lambda,mu)|=(6mu-27lambda)hat(i)-(2mu-27)hat(j)+(2lambda-6)hat(k)`.
`:. (vec(a)xxvec(b))=vec(0)hArr 2lambda-6=0 and 2mu-27=0 hArr lambda=3 and mu = (27)/(2)`.