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Vector analysis

  1. Mar 2, 2013 #1
    Dear all,
    I am new to this forum and this is my first post.
    I hope this is the right place to open this topic.

    I have a homework for my mathematical methods for physics course and i am kind of stuck into a question:

    v=ψ∇β
    show that ∇xv is perpendicular to v.

    Here v is a vector
    x is cross product
    ∇ is gradient vector operator
    ψ and β are non-vectoral functions

    I know it seems obvious, but i need mathematical proof which probably contains some identities of triple cross product with del operator.
    Like i said, i couldn't figure it out.

    Already now, i want to thank you for all your help.
     
    Last edited: Mar 2, 2013
  2. jcsd
  3. Mar 2, 2013 #2

    lurflurf

    User Avatar
    Homework Helper

    hint
    ∇xv=(∇ψ)x(∇β)
    which is obvious from
    ∇x∇β=0
     
  4. Mar 2, 2013 #3
    Hello AdvPhys,


    a) Use the identity of the curl of a scalar function multiplying a vector function
    b) Use the fact that the curl of the gradient of a scalar function is 0
    c) How do you prove that two vectors are perpendicular?
    d) Conclude.

    [Edit: previous post was giving too much info]
     
    Last edited: Mar 2, 2013
  5. Mar 2, 2013 #4
    Thanks for replies.
    But still can't figure out how to conclude the last scalar triple product gives 0.

    Edit: I got that it is obvious. I have the same vector in both parts.

    Again thank you for your help.
     
    Last edited: Mar 2, 2013
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