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April 15th, 2018, 08:46 AM   #1
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The projection of a vector over the orthogonal subspace of other.

Hello I have the vector B = (2,4,1) and want to project it over the orthogonal subspace of another vector, the vector A = (1,1-1).

I did:
(1,1,-1).(2,4,-1) * (1,1,-1) = $\displaystyle 7/3 * (1,1,-1) = (7/3,7/3,-7/3)$
(1,1,-1).(1,1-1)

and then :
$\displaystyle (7/3,7/3,-7/3) - (2,4,1) = (7/3,7/3,-7/3) - (6/3,12/3,3/3) = (1/3,-5/3,-10/3)$

Nonetheless, the correct answer it is: $\displaystyle (1/3,7/3,8/3)$. So what I am doing wrong? Thanks for the input.
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April 15th, 2018, 02:15 PM   #2
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Your first calculation has an error. You used (2,4,-1) instead of (2,4,1). If you do it correctly, you will get the correct answer with a minus sign. This is because your final subtraction is opposite the usual definition.
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