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## Homework Statement

r(t)=(x(t),y(t),z(t))

t has been chosen so that r'.r'=1

show that r'.r''=0

## Homework Equations

v'.w'=|v||w|cos(theta)

## 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.