1. ## a calculus proof

prove that

d/dt(rsub1(t) dot rsub2(t) ) = r'sub1(t) dot r'sub2(t) + rsub1(t) dot r'sub2(t)

Thank you very much

2. The dot here means dot product right? cause if it meant multiply it wouldn't be a prob, it would just be the product rule.

3. Hi Jhevon,

You are right. I got this part. It is actually very simple. Thank you very much.

what about the below part :
use
d/dt(rsub1(t) dot rsub2(t) ) = r'sub1(t) dot r'sub2(t) + rsub1(t) dot r'sub2(t)
to show that for a differentiable 3-space vector valued function r, the graph of r lies on a sphere centered at the orgin if and only if r(t) and r'(t) are orthogonal.

4. If R(t) is on the surface of such a sphere then ||R(t)||=C, is constant.
Taking the derivative we get R’(t)·R(t)/[R(t)·R(t)]=0 or R’(t)·R(t)=0.