Chapter 1, Problem 1.8P

(a)

To determine

Prove that scalar product is distributive that is $\text{r}\cdot \left(\text{u}+\text{v}\right)=\text{r}\cdot \text{u}+\text{r}\cdot \text{v}$.

(b)

To determine

Prove the product rule for differentiating products applied to $\text{r}\cdot \text{s}$ that is $\frac{d}{dt}(r\cdot s)=r\cdot \frac{ds}{dt}+\frac{dr}{dt}\cdot s$.