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Math Help - Simplify and prove, planes

  1. #1
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    Simplify and prove, planes

    Hello.
    I have some questions that I cannot figure out how to solve them.

    Problem 3.5.29)
    Simplify (u+v) x (u-v)

    Problem 3.5.33)
    Prove: If a, b, c and d lie in the same plane, then
    (a x b) x (c x d) = 0

    The "x" meaning the crossproduct.
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  2. #2
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    Quote Originally Posted by algie View Post
    Problem 3.5.29)
    Simplify (u+v) x (u-v)

    Problem 3.5.33)
    Prove: If a, b, c and d lie in the same plane, then
    (a x b) x (c x d) = 0
    For the first one use the distributive property twice.

    For the second one realize that parallel vectors have cross product zero.
    But why are a\times b~\&~c\times d parallel?
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  3. #3
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    The first)
    The distrubutive property, two times?
    u*(v+w) = u*v+u*w
    I do not really understand how to apply it to my problem.

    Here is/was/// my approach at the problem:
    (u+v) x (u-v)
    u^2 -2uv +v^2

    Facit says: 2(v x u)

    The second)
    Because they are perpendicular to the plane.
    I mean, they both go up from the plane so I think thats why they are parallel.
    There is no facit for this, but I think this makes sense.

    Thank you for your help, much appreciated!
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  4. #4
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    Quote Originally Posted by algie View Post
    The first)
    The distrubutive property, two times?
    u*(v+w) = u*v+u*w WRONG
    I do not really understand how to apply it to my problem.
    Here is/was/// my approach at the problem:
    (u+v) x (u-v)
    u^2 -2uv +v^2

    Facit says: 2(v x u)CORRECT
    A\times(B+C)=A\times B + A\times C
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