2026 CJC Promo Q12
2026 CJC Promo Q12
Junior College 1
13 marks
Promo
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]
Solution:
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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 \(\mathbf r=\begin{pmatrix}6\\10\\-1\end{pmatrix}+t\begin{pmatrix}1\\-7\\7\end{pmatrix},\ t\in\mathbb R\).
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