Let F(x,y,z)=(−6xz2,6xyz,6xy3z)F(x,y,z)=(−6xz2,6xyz,6xy3z) be a vector field and f(x,y,z)=x3y2zf(x,y,z)=x3y2z. ∇f=(∇f=( , , )). ∇×F=(∇×F=( , , )). F×∇f=(F×∇f=( , , )). F⋅∇f=F⋅∇f=

Let F(x,y,z)=(−6xz2,6xyz,6xy3z)F(x,y,z)=(−6xz2,6xyz,6xy3z) be a vector field and f(x,y,z)=x3y2zf(x,y,z)=x3y2z. ∇f=(∇f=( , , )). ∇×F=(∇×F=( , , )). F×∇f=(F×∇f=( , , )). F⋅∇f=F⋅∇f=

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 71E

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Question

Let F(x,y,z)=(−6xz2,6xyz,6xy3z)F(x,y,z)=(−6xz2,6xyz,6xy3z) be a vector field and f(x,y,z)=x3y2zf(x,y,z)=x3y2z.
∇f=(∇f=(  ,  , )).
∇×F=(∇×F=(  ,  , )).
F×∇f=(F×∇f=(  ,  , )).
F⋅∇f=F⋅∇f=  .

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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