- #1

goffinj

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## Homework Statement

Find the orthogonal projection of the given vector on the given subspace W of the inner product space V?

V=R3, u = (2,1,3), and W = {(x,y,z): x + 3y - 2z = 0}

I don't understand how to find the orthonormal basis for W?

## Homework Equations

I don't understand how to find the orthonormal basis for W?

I know once you have an orthonormal basis then you know that the projection is just

proj. = <u,v1>*v1 + <u,v2>*v2

where v1,v2 are the orthonormal vectors of the basis for W

## The Attempt at a Solution

Since x + 3y -2z = 0 I took three vectors that are a solution to that system and then used the gram-schmidth to make them orthogonal, then normalized them, then used it to calculate the porjection but it came out wrong. It is supposed to be 1/17*(26 104) where 26 and 104 are in a column vector.

So basically, how to do you find the right basis for W?