# 2022 JPJC J1 MYE Q8

## Timothy Gan

This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.
##### 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 $3x+3y-4z=5$.

[2]

(ii)

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

[3]

(iii)

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

[3]

(iv)

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

[6]

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

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Published: 22nd February 2024
Written by
Timothy Gan
This is Tim. Tim loves to teach math. Tim seeks to improve his teaching incessantly! Help Tim by telling him how he can do better.
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