Your solution seems right. Why do you think it's wrong?
Note that (2, 4, 2, 2) is indeed orthogonal to (2, 1, -5, 1).
ok so I am having a bit of difficulty expanding the answer to this question. since i can't type it out i found it online at this link: http://www.math.ust.hk/~macyfang/hw4.pdf
it's question #2 under section 6.3.
Now I know that I have to decompose v= v^ + z,
but is v^ = (v.u1/u1.u1)x u1? I got v^ to be (2, 4, 2, 2) and z to be (2, 1, -5, 1)
But i am wondering if this is correct, and if my calculation for v^ is correct..
I am thinking that if {u1.... u4} is an orthogonal basis, then the span of {u2, u3, u4} is orthogonal to span {u1}.
But for a 10 mark question, what have i left out??