91Ó°ÊÓ

Find the gradient of the scalar field \(f=x y z\), and evaluate it at the point \((1,2,3)\). Hence find the directional derivative of \(f\) at this point in the direction of the vector \((1,1,0)\).

Find the angle between the surfaces of the sphere \(x^{2}+y^{2}+z^{2}=2\) and the cylinder \(x^{2}+y^{2}=1\) at a point where they intersect.