2022 JPJC J1 MYE Q8
Timothy Gan
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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