Explore BrainMass

Explore BrainMass

    Vectors : Product Rule, Gradient and Curl

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Trying to "prove" the following product rule for vector derivatives given the functions:

    vec{A} = 2x x-hat + y y-hat + 4z z-hat


    vec{B} = 2y x-hat - 3x y-hat

    for the following product rule:

    Del(A.B) [Gradient of A.B] = A X (curl B) + B X (curl A) + (A.Del)B + (B.Del)A

    where I denoted the gradient as Del.

    © BrainMass Inc. brainmass.com March 4, 2021, 7:38 pm ad1c9bdddf

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    = 2x + y + 4z
    = 2y - 3x

    For the following ...

    Solution Summary

    Vectors, Product Rule, Gradient and Curl are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.