The line $l$ passes through $A(3, 1, 4)$ and is parallel to \(2\mathbf{i} + \mathbf{j} + \mathbf

Question

The line $l$ passes through $A(3, 1, 4)$ and is parallel to $2\mathbf{i} + \mathbf{j} + \mathbf{k}$. State the vector equation of $l$.[1] The plane $p$ has equation $$\mathbf{r} \cdot \begin{pmatrix} 2 \ -1 \ -1 \end{pmatrix} = 7.$$ 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) $\mathbf r=\begin{pmatrix}3\1\4\end{pmatrix}+\lambda\begin{pmatrix}2\1\1\end{pmatrix},\ \lambda\in\mathbb R$ (ii) $19.5^\circ$ (iii) $(9,4,7)$ (iv) $\mathbf r=\begin{pmatrix}9\4\7\end{pmatrix}+\mu\begin{pmatrix}2\5\5\end{pmatrix},\ \mu\in\mathbb R$

Vectors - Perpendicular Projection and Reflection in a Plane

Vectors - Perpendicular Projection and Reflection in a Plane

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