Exercise 4.2.2

(a) The projection of $b=(\cos <!--\; FUNCTION\; APPLICATION\; -->𝜃,\sin <!--\; FUNCTION\; APPLICATION\; -->𝜃)$ onto $a=(1,0)$ is $p=(\cos <!--\; FUNCTION\; APPLICATION\; -->𝜃,0)$

(b) The projection of $b=(1,1)$ onto $a=(1,-1)$ is $p=(0,0)$ since $a^{T}b=0$.

The picture for part (a) has the vector $b$ at an angle $𝜃$ with the horizontal $a$. The picture for part (b) has vectors $a$ and $b$ at a $90^{\text{∘}}$ angle.