Multivariable Calc - proof

[Maverick848]

I have no idea how to do this proof:


Let r(t) be a differntiable vector-valued function of t, and let c be a scalar, (and let the period represent the dot product),

If r(t).r(t)=c, then r(t).r'(t)=0

 

[Matt]

\(\displaystyle \L 0=\frac{d}{dt}[r(t)\cdot r(t)]=2r(t)\cdot r'(t)\)