(a) Explain the difference between a scalar and a vector. Provide two examples of each.
(b) Give geometric descriptions of vector addition and scalar multiplication.
(a) Is the weight of a car a scalar or a vector? Explain.
(b) Give geometric proofs of
\[ \begin{align}
(a+b)\textbf{v} &= a\textbf{v} + b\textbf{v} \\
&\text{and} \\
(\textbf{u} + \textbf{v}) + \textbf{w}
&= \textbf{u} + (\textbf{v} + \textbf{w}) \\
\end{align} \]
.