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How can prove this ?

  1. Apr 24, 2007 #1
    All characters are vector quantities

    The question is prove the following equation:

    → → → → → → → → → →
    (2a + b)×(c -a ) + (b + c)×(a × b) = a × c
  2. jcsd
  3. Apr 24, 2007 #2
    Can you put forward any idea that you may have on solving this problem?
  4. Apr 24, 2007 #3
    Why don't you use the asociative, distributive and anticonmutative properties of the cross product?
  5. Apr 24, 2007 #4


    User Avatar
    Science Advisor

    It looks very simple to me by just doing what AiRAVATA says. As you would expect, a loot of things cancel. Look especially carefully at the "anti-commutative" property since you may not be used to that. In particular, what is axa?
  6. Apr 24, 2007 #5
    a x a <=> |a|*|a|*cosθ ,
    because θ=0 so |a|*|a|*cosθ =0 , a x a =0
    Can you give a sample example relative my question? I can not find any example on my schoolbook.
    Thanks you!
    Last edited: Apr 24, 2007
  7. Apr 24, 2007 #6


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    AiRAVATA and HallsofIvy already told you. Expand and it cancels out simply. Have you actually tried it?
  8. Apr 28, 2007 #7
    The reasult is the question is wrong. Someone was sure the question was wrong at frist glance. The question can not be allowd by dimension role.

    (b + c)×(a × b) may change to (b + c)×(a + b)

    In that case, the question was very easy.
  9. Apr 29, 2007 #8
    Surely you mean sinθ, not cosθ. Just wanted to alert you of this mistake... also, that equation only measures the length, since the cross product yields a vector.
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