Answer
$proj_{\textbf{v}}\textbf{u} = <0,-6,3>$
$scal_{\textbf{v}}\textbf{u} = \frac{-15}{\sqrt 5}$
Work Step by Step
$\textbf{u} = <5,0,15>$
$\textbf{v} = <0,4,-2>$
$\textbf{u} \cdot \textbf{v} = (5)(0) + (0)(4) + (15)(-2)= 0 + 0 - 30 = -30$
$\textbf{v} \cdot \textbf{v} = (0)(0) + (4)(4) + (-2)(-2) = 0 + 16 + 4 = 20$
$|\textbf{v}| = \sqrt {(0)^2 + (4)^2 + (-2)^2} = 2\sqrt {5}$
$proj_{\textbf{v}}\textbf{u} = (\frac{\textbf{u} \cdot \textbf{v}}{\textbf{v} \cdot \textbf{v}})\textbf{v} = (\frac{-30}{20})<0,4,-2> = <0,-6,3>$
$scal_{\textbf{v}}\textbf{u} = \frac{\textbf{u} \cdot \textbf{v}}{|\textbf{v}|} = (\frac{-30}{2\sqrt {5}}) = \frac{-15}{\sqrt 5}$
