Vector Calculus

1. Oct 1, 2005

Hey... i was hopeing somebody can help me with a homework question... its about vector calc.... taking the deriviative.

d/dx[r(t) dot r(t)] = r'(t) dot r(t) + r(t) dot r'(t) = 2r'(t) dot r(t)

I know it sounds sillly, but i was just wondering how on earth they got
2r'(t) dot r(t) ????

2. Oct 1, 2005

Hurkyl

Staff Emeritus
Well, go through the list of properties of the dot product -- any of them look useful?

3. Oct 1, 2005

robphy

Another approach... what must be true for that last equality
r'(t) dot r(t) + r(t) dot r'(t) = 2r'(t) dot r(t)
to happen (assuming that each side is correct)?
This should lead to the property hinted by Hurkyl.

4. Oct 4, 2005

Okay i see it now.

It comes from the property....

a dot (b + c) = a dot b + a dot c

:)

Thanks for poinitng that out...

5. Oct 4, 2005

Hurkyl

Staff Emeritus
Ah, right -- that one's so fundamental I forgot it even needed to be invoked! (I had only noticed you needed a.b = b.a)