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Vector question

  1. Oct 16, 2008 #1
    Hi there, i'm a bit stuck on this question:

    " Given 3 non-coplanar vectors a, b and c convince yourself that the position vector r of any point in space may be represented by

    r = λa + μb + γc

    for some real numbers λ, μ and γ.

    Show that

    r.(bxc) = λa.(bxc) ,

    r.(axb) = γa.(bxc) ,

    r.(cxa) = μa.(bxc) . "


    I understand how they get the first one - the cross product of b and c is perpendicular to both of them, so won't contain any b or c components. Hence when you do the dot product you'll be multiplying the b and c bits of r by zero so they disappear. However I don't get the other two...?

    Please help!
     
  2. jcsd
  3. Oct 16, 2008 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    HI kidsmoker! :smile:

    No, you're kidding yourself … you don't understand how they got the first one.

    They got it by dot-producting both sides of r = λa + μb + γ with (bxc).

    Now try dot-producting both sides of r = λa + μb + γ with (axb) instead …

    what do you get? :smile:
     
  4. Oct 16, 2008 #3
    I thought that's what I was doing? axb will be perpendicular to both a and b so won't contain a or b components? So when you dot it with r surely the a and b parts of r will be multiplied by zero?

    Btw did you mean to put r = λa + μb + γc rather than r = λa + μb + γ or am I just confused?

    Thanks.
     
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