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Math Help - Vectors on a plane

  1. #1
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    Question Vectors on a plane

    Hi

    I really need some assistance with the following problem:

    "Find all unit vectors in the plane determined by u = (3,0,1) and v = (1,-1,1) that are perpendicular to the vector w = (1,2,0)".

    The problem for me is that I donīt really know how to approach planes in general. For example, how do I calculate what plane is determined by the two vectors u and v?

    What would u and v look like if they were serparate planes?

    If someone know a website that explains the basics of vector planes I would appreciate the adress.

    Thanks in advance
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  3. #3
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    Quote Originally Posted by Drdumbom View Post
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  4. #4
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    Quote Originally Posted by Drdumbom View Post
    Hi

    I really need some assistance with the following problem:

    "Find all unit vectors in the plane determined by u = (3,0,1) and v = (1,-1,1) that are perpendicular to the vector w = (1,2,0)".

    The problem for me is that I donīt really know how to approach planes in general. For example, how do I calculate what plane is determined by the two vectors u and v?
    Use the cross product: the vector \vec{u}\times \vec{v} is perpendicular to any linear combination of \vec{u} and \vec{v} and, so, is perpendicular to the entire plane. You need to find all unit vectors such that their dot product with that cross product and (1, 2, 0) is 0. That is, take (a, b, c) to be the vector. On condition is that (a, b, c)\cdot(1, 2, 0)= a+ 2b= 0. So you know that a= -2b.
    Now do the same with (a, b, c) and (3,0,1)\times (1,-1,1).

    What would u and v look like if they were serparate planes?

    If someone know a website that explains the basics of vector planes I would appreciate the adress.

    Thanks in advance[/QUOTE]
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