Let `vec(a)=hat(i)+4hat(j)+2hat(k),vec(b)=3hat(i)-2hat(j)+7hat(k)` and `vec(c)=2hat(i)-hat(j)+4hat(k)` . Find a vector `vec(d)` which is perpendicular to both `vec(a)`and `vec(b)`and `vec(c )*vec(d)=15`.

Answer

the required vector `vec(d)=(1)/(3)(160hat(i)-5hat(j)-70hat(k))`