2022 JPJC J1 MYE Q8

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

1. Show that the Cartesian equation of \(p\) is \(3x+3y-4z=5\).[2]
2. Find the acute angle between \(l\) and \(p\).[3]
3. Find the position vector of \(Q\), the foot of perpendicular from point \(C\left( -1,-3,0 \right)\) to \(p\).[3]
4. 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]