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!

Oblique Cross Product

  1. Nov 20, 2014 #1
    1. The problem statement, all variables and given/known data

    Find vector product of [itex]C = A \times B [/itex] of two vectors in oblique coord. system. Give explicit expressions of components of C in covariant and contravariant components (constructing reciprocal basis from direct basis will be useful).

    2. Relevant equations

    I am basically just crossing two vectors, one product is that of two arbitrary contravariant vectors, and one is a product of two arbitrary covariant vectors. I understand this part, I just am always confused by the word "explicit."

    3. The attempt at a solution

    I take this determinant (contravariant)
    [itex] \begin{array}{ccc} a_1 & a_2 & a_3 \\ A^1 & A^2 & A^3 \\ B^1 & B^2 & B^3 \end{array} [/itex]

    and this one as well (covariant)
    [itex] \begin{array}{ccc} a^1 & a^2 & a^3 \\ A_1 & A_2 & A_3 \\ B_1 & B_2 & B_3 \end{array} [/itex]

    and for my covariant components I can set [itex] a_i = \frac{e_i}{sin(\alpha)} [/itex]

    I am not sure what else is being asked, if anything at all.

    I have this relation for components:

    [itex] x_1 = x^1 + x^2cos(\alpha) [/itex]

    but not sure if I should apply it to get vector terms as [itex]a_1A_1 +...[/itex]:
     
  2. jcsd
  3. Nov 23, 2014 #2

    jedishrfu

    Staff: Mentor

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: Oblique Cross Product
  1. Cross product (Replies: 1)

  2. Cross Product? (Replies: 17)

  3. Cross Products (Replies: 6)

  4. Cross Products (Replies: 3)

  5. Cross product (Replies: 3)

Loading...