Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inverse of inner product

  1. Jan 19, 2009 #1
    my question is:

    if a.b=c

    a=any vector
    b=any vector
    .=inner product
    c=resulting scalar

    is there a way to describe a=f(b,c)?

  2. jcsd
  3. Jan 19, 2009 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    No. a isn't completely determined by b and c, since you can replace a with a+d in your first equation, if d is orthogonal to b.
  4. Jan 19, 2009 #3

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    No. Think of it this way: Suppose you find vectors a and d such that a.b = c and d.b=0 (i.e., d is orthogonal to b). Then for any scalar k, (a+k*d).b=c also. In other words, the solution to a.b=c is not unique.
  5. Jan 19, 2009 #4
    Ok thanks!

    but it did not solve my problem regarding vortex dynamics....

    I would like to use the the law of Biot and Savart to determine the velocity field induced by a vortex filament. I am trying to do this by rewriting the equation of the circulation to a function for the vorticity.

    To do this, I am using the Dirac Delta function for another integral for the circulation. This way i can equal the two integrands. But from that expression I would like to write the vorticity as a function of the rest (to substitute it in Biot ans Savart). But from your explanations I see that this is not possible??

    Attached Files:

  6. Jan 19, 2009 #5
    already solved it....

    w.n = the magnitude of the vector=length(w)
    dx/ds / length(dx/ds) = unity direction of the vector

    so the vector is w is determined to be (w.n)*(dx/ds / length(dx/ds))
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook