Question

How do I find the orthogonal projection of a vector?

Answer 1

The orthogonal projection of `vec{a}` onto `vec{b}` can be found by

`(vec{a}cdot vec{b}/|vec{b}|)vec{b}/|vec{b}|={vec{a}cdot vec{b}]/{vec{b}cdot vec{b}}vec{b}`

Let us find the orthogonal projection of `vec{a}=(1,0,-2)` onto `vec{b}=(1,2,3)`.

`{(1,0,-2)cdot(1,2,3)}/{(1,2,3)cdot(1,2,3)}(1,2,3)={-5}/{14}(1,2,3)=(-5/14,-10/14,-15/14)`.

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I hope that this was helpful.