Find the volume of parallelopiped, whose sides are given by vectors `hat(i) + hat(j) + hat(k) and 3hat(i) - hat(j) + 2 hat(k)`, Also, find `lambda`, such that the vectors `hat(i) + 2hat(j) + 3 hat(k), 4 hat(i) + hat(j) + lambda hat(k) and lambda hat(i) + hat(k)` are coplanar.

Answer

`lambda -5, lambda = - (11)/(2)`