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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- Mar 8th 2011, 06:44 PMSherinaFind 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 - Mar 8th 2011, 09:00 PMTinyboss
Inner product zero is the same as perpendicular--does that help?

- Mar 9th 2011, 04:22 AMHallsofIvy
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.

- Mar 9th 2011, 05:07 AMAckbeet
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.