# Inner product orthogonal vectors

1. Sep 28, 2011

### derryck1234

1. The problem statement, all variables and given/known data

Let R4 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?

2. Sep 28, 2011

### dynamicsolo

That might be because what you wrote is not a unit vector (which is what the problem asks for). [That is to say, t is not completely arbitrary...]

Now that I check, you'll find that your components do not solve the second and third of your linear equations (especially not the third one!).

[Small hint: you should be getting 11's in your denominators.]

Last edited: Sep 28, 2011