For this question, I started with the dot product of an arbitrary vector u and v:
u•v
= ||u|| ||v|| cos(45)
= (1) (√2) (√2/2)
= 1
Then I used the u1v1 + ... + u3v3 = 1 property, and then subbed in u1 = 1 - u3 into the ||u|| formula, more subbing... and ended up with a vector all in terms of u3: u = [ 1 - u3 , √(2•u3), u3 ] where 0 <= u3 <= 1 . Is this final answer correct? The answer I was given says that the answer is (cosx , sinx, 0) , but that can't be right since it asks for all vectors unit vectors, and obviously (0, 0, 1) would work.