Answer to Question #231910 in Vector Calculus for ADDY

Question #231910

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


1
Expert's answer
2021-09-02T00:35:46-0400
"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"


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