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Vector Cross Product

  1. Sep 16, 2007 #1
    1. The problem statement, all variables and given/known data

    Given that A = 2i + 4j, evaluate each of the following. (Hint: This question can be answered without computation.)

    (a) What is AxB when B = 8i + 16j?

    (b) What is AxB when B = -8i - 16j?

    2. Relevant equations

    AxB=(Axi + Ayj) x (Bxi +Byj)
    =(AxBx)(i x i) + (AxBy)(i x j) + (AyBx)(j x i) + (AyBy)(j x j)
    AxB=(AxBy - AyBx)k

    3. The attempt at a solution

    AxB= (2 x 16)k - (4 x 8)k= 0k
     
  2. jcsd
  3. Sep 16, 2007 #2

    arildno

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    Indeed.

    Can you see the relation between A and B that makes the zero result trivial, i.e you can solve it "without" computation?
     
  4. Sep 16, 2007 #3
    They have the same/opposite direction?
     
  5. Sep 16, 2007 #4
    Geeze no kidding! dahh. Thanks
     
  6. Sep 16, 2007 #5

    arildno

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    Indeed.
    The vectors involved are parallell. Therefore, their cross product must be 0.
     
  7. Sep 16, 2007 #6

    Astronuc

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    Try parallel or colinear. They are scalar multiples of the same unit vector.
     
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