Exercise 6

What is the orthogonal projection of $\vec{v}$ into a line if $\vec{v}$ is a member of that line?

Show that if $\vec{v}$ is not a member of the line then the set $\{\hskip 1.00006pt\vec{v},\vec{v}-\text{proj}_{[\vec{s}\,]}({\vec{v}\,})\hskip 1.00006pt\}$ is linearly independent.