mark
Let \vec{u} = \langle -2,1 \rangle and let v = \langle 1,5 \rangle. Express
\vec{v} = \vec{v}_{\|} + \vec{v}_{\perp},
where \vec{v}_{\|} is parallel to \vec{u} and \vec{v}_{\perp} is perpendicular to \vec{u}.
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Vector projection
mearing
proj\vec{u}^{\vec{v}}=\frac{-2+5}{5}\langle-2,1\rangle
\vec{v}_{\|}=\langle-\frac{6}{5},\frac{3}{5}\rangle
\langle1,5\rangle=\langle-\frac{6}{5},\frac{3}{5}\rangle+\vec{v}_{\perp}
\vec{v}_{\perp}=\langle\frac{11}{5},\frac{22}{5}\rangle