How do I find the orthogonal projection of two vectors?

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How do I find the orthogonal projection of two vectors?

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Answer 1 · 2015-05-03T19:55:30

The question perhaps is about projection of some $\to b$ $vecb$ on another $\to a$ $veca$ in the same vector space. If this projection is vector $\to p$ $vecp$ , then set the vector dot product $\to a$ $veca$ and ( $\to b$ $vecb$ - $\to p$ $vecp$ ) equal to 0, because $\to a$ $veca$ and $\to b$ $vecb$ - $\to p$ $vecp$ would be orthogonal.

Since $\to p$ $vecp$ is along $\to a$ $veca$ , it would be some multiple of $\to a$ $veca$ . let it be x

Thus $\to a . (\to b - x \to a)$ $veca. (vecb-xveca)$ =0, x= $\frac{\to a . \to b}{| a | | a |}$ $(veca.vecb)/(|a||a|)$

Hence $\to p$ $vecp$ = x $\to a$ $veca$ = $\frac{\to a . \to b}{| a | | a |} \to a$ $(veca.vecb)/(|a||a|) veca$

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How do I find the orthogonal projection of two vectors?

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