Linear Algebra Question

1. Sep 15, 2008

kuahji

Find u.v given that ||u+v||=1 & ||u-v||=5.

The first thing I did was drawn a simple picture, it became apparent that u & v wouldn't be orthogonal. So then the Pythagorean Theorem wouldn't work. Next I moved on to squaring both sides
||u+v||$$^{2}$$=||u||$$^{2}$$+2(u.v)+||u||$$^{2}$$
However here again, I didn't seem to be getting anywhere because I can't do anything with the middle term. I also tried squaring the other equation, solving for ||u|| & substituting it into the other equation. But that still left me with two variables in one equations. So I'm kinda lost about what to actually do in this problem.

2. Sep 15, 2008

Dick

There isn't any unique solution. If you find a u and v that satisfy that then you can always rotate u and v by any angle and they will still satisfy that relation. Are you just supposed to find ANY u and v?

3. Sep 15, 2008

kuahji

Yes any solution. We had a similar one earlier that had infinitely many solutions. But it was specified that it was R^2 or R^3. Here it does not say. We haven't learned about rotations yet, that is the next section.

4. Sep 15, 2008

Dick

How about R^1? u=3, v=-2. Is that good enough? If it's R^2, u=(3,0), v=(-2,0). Etc.