 # 2022 JPJC J1 MYE Q8 # 2022 JPJC J1 MYE Q8 ##### 2022 JPJC J1 MYE Q8

The plane $p$ passes through the points $A\left( 1,2,1 \right)$ and $B\left( 0,3,1 \right)$ is parallel to the vector $\mathbf{i}+3\mathbf{j}+3\mathbf{k}$. The line $l$ has equation $\frac{x-1}{2}=2-y=z-1$.

(i)

Show that the Cartesian equation of $p$ is $3x+3y-4z=5$.



(ii)

Find the acute angle between $l$ and $p$.



(iii)

Find the position vector of $Q$, the foot of perpendicular from point $C\left( -1,-3,0 \right)$ to $p$.



(iv)

Find the area of triangle $ABQ$ and hence, find the volume of the pyramid, $CABQ$.



[Volume of pyramid$=\frac{1}{3}\times$Base Area$\times$Perpendicular Height]

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Published: 8th August 2023 Written by
Timothy Gan
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