Let u and v be unit vectors. Prove that u+v is perpendicular to u − v.
What I did is:
Since they are unit vectors: $|u|$=$|v|$=1
If they are perpendicular, then $(u+v)$.$(u-v)$=$0$
Ans: $|u+v|$.$|u-v|$.$\cos\theta$
= (1+1).(1-1).$\cos\theta$
=$0$
proved.
Is this right?
No, it is not right, because $|u+v|$ is not $|1+1|$.
Try this, instead: $$(u+v)\cdot(u-v)=u\cdot u+u\cdot v-v\cdot u-v\cdot v=\ldots$$