Orthogonality of time dependent vector derivatives of constant magnitude

[lordkelvin]

I'm having trouble understanding why a derivative of a time dependent vector function is orthogonal to the original function. Can anybody give me some enlightenment? I searched around for some previous talk about this, and I can't find anything.

Thanks.

 

[Petr Mugver]

You have to be a bit more specific... I don't understand your question right now.

 

[George Jones]

Does the time-dependent vector have constant magnitude?

 

[lordkelvin]

Yes the original vector function is of constant magnitude. Take a vector function r(t) of constant magnitude and then r dot should be orthogonal to r. I don't understand why.

 

[George Jones]

Take the derivative with respect to time of both sides of

r^2 = \bold{r}\left( t \right) \cdot \bold{r}\left( t \right).

What do you get?