Find the matrix for the transformation that projects each point in R3 (3-D) perpendicularly onto the plane 7x + y + 3z = 0 .(adsbygoogle = window.adsbygoogle || []).push({});

The attempt at a solution is attached for question 1 (actually instructor's solution)

I kind of understand it but ...

why is n <dot> v = equation of the plane?

Does v represent all of the possible points of R^3 (certainly does not seem so...) which is projected to the normal?

I understand the v-projection is there to get the projection of v onto the plane because we cannot directly project to the plane right? But why do we want v' what does v' represent and how is that the solution?

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# Linear Algebra Matrix Transformation to plane

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