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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 $$\mathbf{u}$$?

Mar 21, 2020