Question

A= x²zi + xy j +y²z k, B = yz² +xz j + x²z k, find grad(A.B)

Answer 1

$$A\cdot B=x^2z(yz^2)+xy(xz)+y^2z(x^2z)$$

$$=x^2yz^3+x^2yz+x^2y^2z^2$$

$$grad(A\cdot B)=\nabla(A\cdot B)$$

$$=\langle\dfrac{\partial}{\partial x}(A\cdot B), \dfrac{\partial}{\partial y}(A\cdot B),\dfrac{\partial}{\partial z}(A\cdot B)\rangle$$

$$=(2xyz^3+2xyz+2xy^2z^2)i$$

$$+(x^2z^3+x^2z+2x^2yz^2)j$$

$$+(3x^2yz^2+x^2y+2x^2y^2z)k$$