The points $A$ and $B$ have coordinates $(2, 1, -1)$ and $(5, -1, 3)$ respectively. Find a v

Question

The points $A$ and $B$ have coordinates $(2, 1, -1)$ and $(5, -1, 3)$ respectively. Find a vector equation of the line $AB$.[1] The point $C$ has coordinates $(10, -2, 6)$. Find the position vector of the foot of perpendicular from $C$ to the line $AB$.[3] Find a vector equation of the line which is a reflection of the line $AC$ in the line $AB$.[3]

Accepted Answer

(a) $\mathbf r=\begin{pmatrix}2\1\-1\end{pmatrix}+\lambda\begin{pmatrix}3\-2\4\end{pmatrix},\ \lambda\in\mathbb R$ (b) $\overrightarrow{ON}=\begin{pmatrix}8\-3\7\end{pmatrix}$ (c) $\mathbf r=\begin{pmatrix}2\1\-1\end{pmatrix}+\mu\begin{pmatrix}4\-5\9\end{pmatrix},\ \mu\in\mathbb R$

Vectors - Perpendicular Projection and Reflection in a Line

Vectors - Perpendicular Projection and Reflection in a Line

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