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Math Help - Find vectors using the euclidean norm and inner product.

  1. #1
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    Find vectors using the euclidean norm and inner product.

    Hi I'm not really sure how to do this:

    find two vectors in R^2 with Euclidean norm 1 whose euclidean inner product with (3, -1) is zero
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  2. #2
    Senior Member Tinyboss's Avatar
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    Inner product zero is the same as perpendicular--does that help?
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  3. #3
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    Or- the inner product of vector (x, y) with (3, -1) is 3x- y. Your problem is just two find two separate values for (x, y) such that 3x- y= 0. Unless there is some other condition you did not mention, there are an infinite number of possible answers.
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  4. #4
    A Plied Mathematician
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    Due to the fact that the Euclidean norms of the vectors found all have to be one, it follows that in two dimensions, there are exactly two solutions.
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