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Consider the line through points A = (1, 1, 2) and B = (2, 3, 4), and let P be the foot of the perpendicular from Q = (3, -7, -1) to this line, as in the picture below:

Then \(\overrightarrow{AP}\)  is the projection of \(\overrightarrow{AQ}\) onto a vector \(\mathbf{u} = \begin{pmatrix} u_1 \\ u_2 \\ u_3 \end{pmatrix}\)
such that \(u_1 + u_2 + u_3 = 5.\) What is u?

 Apr 1, 2019
 #1
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The answer is [-2,4,5].

 Nov 3, 2019

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