The line $l$ passes through $A(1, 2, -1)$ and is parallel to $3\mathbf{i} + 3\mathbf{k}$. Stat

Question

The line $l$ passes through $A(1, 2, -1)$ and is parallel to $3\mathbf{i} + 3\mathbf{k}$. State the vector equation of $l$.[1] The plane $p$ has equation $$\mathbf{r} \cdot \begin{pmatrix} 1 \ -2 \ 2 \end{pmatrix} = 13.$$ Find the acute angle between $l$ and $p$.[2] Find the point of intersection of $l$ and $p$.[2] Find the vector equation of the reflection of $l$ in $p$.[6]

Accepted Answer

(i) $\mathbf r=\begin{pmatrix}1\2\-1\end{pmatrix}+\lambda\begin{pmatrix}1\0\1\end{pmatrix},\ \lambda\in\mathbb R$ (ii) $45^\circ$ (iii) $(7,2,5)$ (iv) $\mathbf r=\begin{pmatrix}7\2\5\end{pmatrix}+\mu\begin{pmatrix}1\4\-1\end{pmatrix},\ \mu\in\mathbb R$

Vectors - Perpendicular Projection and Reflection in a Plane

Vectors - Perpendicular Projection and Reflection in a Plane

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