Gram-Schmidt Orthogonalization Process

Okay, so my textbook asks me to "verify that the basis B for the given vector space is orthogonal.  Use theorem 7.5 as an aid in finding the coordinates of the vector u relative to the basis B.  Then write u as a linear combination of the basis vecotrs."
B={<1,0,1>,<0,1,0>,<-1,0,1>,R3;
u=<10,7,-13>
For reference, *=dot product
For reference, theorem 7.5 states that B = {w1,w2,...,wn} is an orthonormal basis for Rn.  If u is any vector in Rn then u=(u*w1)w1+(u*w2)w2+...(u*wn)wn.


Now I wasn't entirely sure what It was asking, but I tried anyway.
Ok, so lets say v1=<1,0,1>,v2=<0,1,0>,v3=<-1,0,1>:
To prove orthogonality, I say v1*v2=0,v2*v3=0,v1*v3=0, right?
Next I try using theorem 7.5.  This is where things go wrong.
I get u=<10,7,-13>=-3v1+7v2-23v3=<20,7,-26>
Now, this doesn't equal u.
Also, the solutions in the back of my book just has "-3/2v1+7v2-23/2v3" written, and It uses the same v1,v2,v3.

My book is retarded and doesn't have any equivalent examples, so I turn to you for help.  What the fuck did I do wrong and how do I fix it?

You were pretty close actually. Where you went wrong is using merely an orthogonal basis where the Theorem (I can't believe that's a theorem btw!) asks for an othonormal basis to be used.

The trick is to normalise your v1, v2, v3. v2 is already normalised, but v1 and v3 will have to be scaled.

Once you've used the Theorem, you can "un-scale" the v's to get the linear combination you want.

And how do I do this?  Just convert to a unit vector?

I guessed right.  Thanks for the advice.

I owe you one small favour.