Question 1302e

Vectors II: Lines and Planes

Foot of Perpendicular and Reflection in Lines

Question

The line

{l}

is given by

l: \mathbf{r} = \begin{pmatrix} 1 \\ 4 \\ - 4 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}, \; \lambda \in \mathbb{R}.

Find the coordinates of the foot of perpendicular,

{F,}

from the point

{B \left( 1, 0, - 12 \right)}

to the line

{l.}

{F}

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