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Let b=(3,1,1) and P be the plane through the origin given by x+y+2z=0.

(a) Find an orthogonal basis for P. That is, find two nonzero orthogonal vectors V[itex]_{1}[/itex], V[itex]_{2}[/itex] [itex]\in[/itex] P.

(b)find the orthogonal projection of b onto P. That is, find Proj[itex]_{V_{1}}[/itex]b+Proj[itex]_{V_{2}}[/itex]b.

## Homework Equations

[itex]\vec{P}[/itex]=([itex]\vec{v}[/itex][itex]\bullet[/itex][itex]\vec{a}[/itex]/||[itex]\vec{a}||^{2}[/itex])[itex]\vec{a}[/itex]

## The Attempt at a Solution

I have no idea where to even begin. I tried looking up what an orthogonal basis is, but everywhere I looked they used topological symbols I wasn't the slightest bit familiar with. It's also not in my book. I know how to solve for an orthognonal projection for the most part by using the equation above, but I really have no idea what an orthogonal prjection actually is or what its significance is. I really don't want anyone to just give me the answer. I really need to understand this all. Thank you!