The line $l$ has vector equation \[l : \mathbf{r} = \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix} + \

Question

The line $l$ has vector equation $$l : \mathbf{r} = \begin{pmatrix} 1 \ 2 \ -1 \end{pmatrix} + \lambda \begin{pmatrix} 2 \ -1 \ 2 \end{pmatrix} , \quad \lambda \in \mathbb{R}.$$ Find the position vector of the point $N$, the foot of perpendicular from the point $A(6, 4, 4)$ to the line $l$.[3] Find the position vector of the point $A'$, the reflection of $A$ in the line $l$.[2] Find the coordinates of the points on the line $l$ that are $3\sqrt{3}$ units away from point $A$.[2]

Accepted Answer

(a) $\overrightarrow{ON}=(5,0,3)$ (b) $\overrightarrow{OA'}=(4,-4,2)$ (c) $(3,1,1)$ and $(7,-1,5)$

Vectors - Perpendicular Projection and Reflection in a Line

Vectors - Perpendicular Projection and Reflection in a Line

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