In my multivariable calculus class we have several practice problems where given a vector valued function r(t): we need to find $$r'(t) \cdot r''(t)$$
$$r'(t) \times r''(t)$$
For example, using the given function $r(t) = cos(t)i +sin(t)j +2tk$ which is from Larson 10e section 12.2 example 2.
The book seems to emphasize this calculation in the exercises and because of the frequency with which it appears, I wonder if this calculation has any significance. Is this just a convenient way for the authors to practice dot products, cross products, and derivatives of vector functions, or is there a meaning in math or any other field to taking the dot or cross product of a first derivative with a second derivative. I know how to solve the calculation, my question is whether there is any meaning to it.