Calculus 3 - Vector Projections & Orthogonal Components

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1:30For a nonzero reference vector v, split u into a component parallel to v and another perpendicular to v. These directions are relative to v, not necessarily the coordinate axes.

4:30For $u=(3,5)$ and $v=(2,4)$, the coefficient is ($u\cdot v$)/($v\cdot v$)=$26/20=13/10$. The projection is ($13/5$,$26/5$).

6:00Subtracting the projection gives ($2/5$,−$1/5$). Its dot product with v is zero, confirming that the remaining component is orthogonal.

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