If `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(p)` which is perpendicular to both `vec(a)` and `vec(b)` and `vec(p).vec(c) = 18`.

Answer

`vec(p) = 64hat(i)-2hat(j) - 28hat(k)`