The line $l$ passes through point $A(3,1,2)$ and is in the direction \(\begin{pmatrix}1\3\-1\e

Question

The line $l$ passes through point $A(3,1,2)$ and is in the direction $\begin{pmatrix}1\3\-1\end{pmatrix}$. The plane $p$ passes through point $B(3,4,5)$ and is perpendicular to $\begin{pmatrix}2\1\2\end{pmatrix}$. Find a cartesian equation of the plane $p$.[2] Find the acute angle between $l$ and $p$.[2] Find the point of intersection between $l$ and $p$.[3] Find the position vector of the foot of perpendicular from $A$ to $p$. Hence find the equation of the reflected line of $l$ in the plane $p$.[6]

Accepted Answer

(a) $2x+y+2z=20$. (b) $17.5^\circ$. (c) $(6,10,-1)$. (d) $\overrightarrow{ON}=\begin{pmatrix}5\2\4\end{pmatrix}$; reflected line $\mathbf r=\begin{pmatrix}6\10\-1\end{pmatrix}+t\begin{pmatrix}1\-7\7\end{pmatrix},\ t\in\mathbb R$.

2026 CJC Promo Q12

2026 CJC Promo Q12

Solution:

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