Answer
see the details.
Work Step by Step
(a) We have to check the following properties;
For any vectors $u,v,w$ in the given space and $ k \in {R}$;
(1) $\langle u,u\rangle\geq0$ and $\langle u,u\rangle= 0$ if and only if $u=0$.
(2) $\langle u,v\rangle=\langle v,u\rangle$.
(3) $\langle k u,v\rangle=k\langle u,v\rangle$.
(4) $\langle u+v,w\rangle=\langle u,w\rangle+\langle v,w\rangle$.
(b) The orthogonal projection of $u$ onto $v$ is given by
$$\operatorname{proj}_{{v}} {u}
=\frac{\langle{u}, {v}\rangle}{\langle{v}, {v}\rangle} {v}$$
