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# Show that the vector $orth_a b = b - proj_a b$ is orthogonal to $a$. (It is called an orthogonal projection of $b$.)

## $\mathbf{a} \cdot$ ortho $\mathbf{b}=\mathbf{a} \cdot \mathbf{b}-\frac{\mathbf{a} \cdot \mathbf{b}}{|\mathbf{a}|^{2}} \mathbf{a} \cdot \mathbf{a}$$a \cdot ortho _{\mathrm{a}} \mathrm{b}=\mathrm{a} \cdot \mathrm{b}-\mathrm{a} \cdot \mathrm{b}$$\mathbf{a} \cdot \mathbf{b}=0 \quad$ (R.T.P)

Vectors

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##### Top Calculus 3 Educators  ##### Heather Z.

Oregon State University ##### Samuel H.

University of Nottingham Lectures

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### Video Transcript

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Vectors

##### Top Calculus 3 Educators  ##### Heather Z.

Oregon State University ##### Samuel H.

University of Nottingham Lectures

Join Bootcamp