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

B Does the following cross product identity always work?

  1. Oct 16, 2016 #1
    Mod note: Reproduced contents of image with broken link:
    i = j x k
    j = k x i
    k = i x j

    Wikipedia says this about the standard basis vectors. Does this work for all (i.e, non basis) vectors? For example, if you know A = B X C does that mean C = A X B and B = C X A?
     
    Last edited by a moderator: Oct 17, 2016
  2. jcsd
  3. Oct 16, 2016 #2
    Nope. Let's start with ##A = B \times C## and see what ##A \times B## gives us. Using the vector triple product identity, we have ##A \times B = (B\times C) \times B = C (B\cdot B) - B (B \cdot C)##. So, ##A \times B = C## only if ##B## and ##C## are orthogonal (i.e. their dot product is zero) - which is true for the standard basis vectors, but not true in general.
     
  4. Oct 16, 2016 #3

    fresh_42

    Staff: Mentor

    Have you tried ##A=0##?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Does the following cross product identity always work?
  1. Cross Product (Replies: 6)

  2. Cross product (Replies: 2)

Loading...