1. The problem statement, all variables and given/known data r(t)=(x(t),y(t),z(t)) t has been chosen so that r'.r'=1 show that r'.r''=0 2. Relevant equations v'.w'=|v||w|cos(theta) 3. The attempt at a solution Clearly what is being described is circular motion about a unit circle. And using the equation for a unit circle its easy to show that r'.r''=0 Velocity is tangent to the circle, acceleration is inward and therefore the dot product of the two is zero. What I am having trouble with is showing for the general solution. r'.r'=|r'||r'|cos(theta) = 1 theta is zero, and therefore |r'| is 1 , this isn't particularly helpful. r''.r'=|r''|cos(theta) (theta not zero) Expanding in parametric form doesn't seem to help either. r''.r'= x'(t)x''(t)+y'(t)y''(t)+z'(t)z''(t) I am at a loss.