- #1
kuahji
- 394
- 2
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||[tex]^{2}[/tex]=||u||[tex]^{2}[/tex]+2(u.v)+||u||[tex]^{2}[/tex]
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.
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||[tex]^{2}[/tex]=||u||[tex]^{2}[/tex]+2(u.v)+||u||[tex]^{2}[/tex]
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.