Find the projection of u = [-3 1] onto the unit vector v = [1/√2 1/√2].

Question

Find the projection of [latex]\vec{u}[/latex] = [latex]\left [ \begin{matrix} -3 \ 1 \end{matrix} ight ][/latex] onto the unit vector [latex]\vec{v}[/latex] = [latex]\left [ \begin{matrix} 1/\sqrt{2} \ 1/\sqrt{2} \end{matrix} ight ][/latex].

Accepted Answer

We have

[latex]proj_{\vec{v} }(\vec{u} ) = (\vec{v}\cdot \vec{u} )\vec{v}[/latex]

= [latex]\left(\frac{-3}{\sqrt{2} } + \frac{1}{\sqrt{2} } ight) \left [ \begin{matrix} 1/\sqrt{2} \ 1/\sqrt{2} \end{matrix} ight ][/latex]

= [latex]\frac{-2}{\sqrt{2} } \left [ \begin{matrix} 1/\sqrt{2} \ 1/\sqrt{2} \end{matrix} ight ][/latex]

= [latex]\left [ \begin{matrix} -1 \ -1 \end{matrix} ight ][/latex]

Question 1.5.5: Find the projection of u = [-3 1] onto the unit vector v = [...

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