(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let R^{4}have the Euclidean inner product. Find two unit vectors that are orthogonal to the three vectors

u= (2, 1, -4, 0) ;v= (-1, -1, 2, 2) ;w= (3, 2, 5, 4)

2. Relevant equations

<u,v> = u1v1 + u2v2 + u3v3 + u4v4 = 0 {orthogonal}

3. The attempt at a solution

There is no example in the textbook for this kind of problem.

What I thought of doing was making three sets of linear equations. By letting a orthogonal vector be = (x, y, z, w), therefore:

2x + y - 4z = 0

-x -y + 2z + 2w = 0

3x + 2y + 5z + 4w = 0

The general solution to which I found to be:

t(-310/3, 4/3, -154/3, 1)

This does not agree with the back of the textbook?

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# Inner product orthogonal vectors

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