1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Short (I think) vector calculus question

  1. Feb 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Calculate the following expressions:

    question.png

    2. Relevant equations

    3. The attempt at a solution

    Letting the vector a = (a_1, a_2, a_3) I've worked out that it's 2|a|^2

    While that method is fairly quick, I don't particularly like it, and was wondering if there is a shorter or neater method using identities and such, perhaps using del^2 = del . del, then using div and grad identities? Cheers.
     
  2. jcsd
  3. Feb 20, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You could work it out as div(grad((a.r)^2)), but it amounts to doing the pretty much the same thing you just did.
     
  4. Feb 21, 2012 #3
    Yeah, that's what I thought. But wasn't sure if there was a way to simplify grad((a.r)^2)
     
  5. Feb 21, 2012 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    grad((a.r)^2)=2(a.r)*grad(a.r)=2(a.r)a. div(2(a.r)a)=a.grad(2(a.r))+2(a.r)div(a)=2a.a+0=2a.a. You can write down all the steps with vectors, but I really don't think it's saving much time.
     
    Last edited: Feb 21, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Short (I think) vector calculus question
Loading...