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April 15th, 2018, 07:46 AM  #1 
Newbie Joined: Jan 2018 From: brazil Posts: 4 Thanks: 0  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 = (1,11). 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).(1,11) 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. 
April 15th, 2018, 01:15 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,787 Thanks: 708 
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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orthogonal, projection, subspace, vector 
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