Answer
$⟨-\frac{4}{5},0,-\frac{2}{5}⟩$
Work Step by Step
Projection of $\textbf{u}$ along $\textbf{v}=\textbf{u}_{||\textbf{v}}$$=(\frac{\textbf{u}\cdot\textbf{v}}{||\textbf{v}||^{2}})\textbf{v}$
$\textbf{u}\cdot\textbf{v}=⟨-1,2,0⟩\cdot ⟨2,0,1⟩=-1\times2+2\times0+0\times1=-2$
$||\textbf{v}||^{2}=(\sqrt {2^{2}+0^{2}+1^{2}})^{2}=2^{2}+1^{2}=5$
Then, $\textbf{u}_{||\textbf{v}}=(-\frac{2}{5})\,⟨2,0,1⟩=⟨-\frac{4}{5},0,-\frac{2}{5}⟩$
