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} 2 \\ - 1 \\ 3 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}, \; \lambda \in \mathbb{R}.

Find the coordinates of the point,

{B',}

obtained when the point

{B \left( - 6, - 2, 18 \right)}

is reflected in the line

{l.}

{B'}

{\Big(}

{\Big)}