Thread: 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

Inner product zero is the same as perpendicular--does that help?

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.

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.