Let \vec{v} = \left [ \begin{matrix} 2 \\ 1 \\ 1 \end{matrix} \right ] and \vec{u} = \left [ \begin{matrix} 1 \\ 5 \\ 1 \end{matrix} \right ]. Determine proj_{\vec{v} }(\vec{u} ) and perp_{\vec{v} }(\vec{u} ).
Question 1.5.8: Let v = [2 1 1] and u = [1 5 1].Determine projv(u) and perpv...
proj_{\vec{v} }(\vec{u} ) = \frac{\vec{v} \cdot \vec{u} }{\left\|\vec{v} \right\| ^{2} } \vec{v} = \frac{8}{6}\left [ \begin{matrix} 2 \\ 1 \\ 1 \end{matrix} \right ]=\left [ \begin{matrix} 8/3 \\ 4/3 \\ 4/3 \end{matrix} \right ]
perp_{\vec{v} }(\vec{u} ) = \vec{u} – proj_{\vec{v} }(\vec{u} ) = \left [ \begin{matrix} 1 \\ 5 \\ 1 \end{matrix} \right ] – \left [ \begin{matrix} 8/3 \\ 4/3 \\ 4/3 \end{matrix} \right ] = \left [ \begin{matrix} -5/3 \\ 11/3 \\ -1/3 \end{matrix} \right ]
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