**Prove that v(t) is any vector that depends on time (for example the velocity of a moving particle) but which has constant magnitude, then [tex]\dot{v}[/tex](t) is orthogonal to v(t). Prove the converse that if [tex]\dot{v}[/tex](t) is orthogonal to v(t), then lv(t)l is constant. Hint: consder the derivative of v^2.**

This is a very hand result. It explains why, in 2-D polars, d[tex]\hat{r}[/tex]/dt has to be in the direction of [tex]\hat{\phi}[/tex] and vice versa. It also shows that the speed of a charged particle in a magnetic field is constant, since teh acceleration is perpendicular to the velocity.

This is a very hand result. It explains why, in 2-D polars, d[tex]\hat{r}[/tex]/dt has to be in the direction of [tex]\hat{\phi}[/tex] and vice versa. It also shows that the speed of a charged particle in a magnetic field is constant, since teh acceleration is perpendicular to the velocity.

How to I approach proving this? I'm also unclear on Orthogonal, which I'll look up now but if someone could explain this to compliment what I'm off to figure out, I'd appreciate it a great deal.

Thanks!