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Math Help - Vector Orthogonality

  1. #1
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    Vector Orthogonality

    Hey guys! I have a question which is pretty straightforward but I'm not sure how to prove it...

    Show that for any vectors a, b, and c, vector v = b(a*c) - c(a*b) is orthogonal (perpendicular) to a

    There is this theorem which states that if 3 vectors are coplanar, their triple product is equal to 0
    Also, If a, b, and c are coplanar, then b * c will be orthogonal to a, hence their dot product will be equal to 0

    That's all I could find and I'm not sure if I just prove it by theorem or if i have to do some arithmetic
    Any help would be greatly appreciated!
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  2. #2
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    Re: Vector Orthogonality

    I think I know what question you're asking, but you should be careful with the * operation. Does * refer to a cross product or dot product? a*c would most likely be interpreted as a dot product, while a \times c is clearly a cross product.
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  3. #3
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    Re: Vector Orthogonality

    I'm not too sure. In the question there is a period in between the letters which means to multiply
    Edit: Looks like it is a dot product
    Last edited by hemster83; September 25th 2012 at 07:55 PM.
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  4. #4
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    Re: Vector Orthogonality

    Quote Originally Posted by hemster83 View Post
    Show that for any vectors a, b, and c, vector v = b(a\cdot c) - c(a\cdot b) is orthogonal (perpendicular) to a

    There is this theorem which states that if 3 vectors are coplanar, their triple product is equal to 0
    You don't need the triple product theorem. Just note that:
    (v\cdot a) = (b\cdot a)(a\cdot c) - (c\cdot a)(a\cdot b)=0~.
    Thanks from hemster83
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  5. #5
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    Re: Vector Orthogonality

    Quote Originally Posted by Plato View Post
    You don't need the triple product theorem. Just note that:
    (v\cdot a) = (b\cdot a)(a\cdot c) - (c\cdot a)(a\cdot b)=0~.
    Thank you for the help!
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