2022 MI P2 Q4

The equations of the plane \({{\pi }_{1}}\) and the line \(l\) are \(\mathbf{r}\cdot \left( \begin{matrix} 1 \\ 0 \\ 1 \\ \end{matrix} \right)=1\) and \(\frac{x}{2}=y+1\), \(z=2\) respectively. The plane \({{\pi }_{2}}\) contains the line \(l\) and the point \(A\) with position vector \(\left( \begin{matrix} -1 \\ 0 \\ 1 \\ \end{matrix} \right)\), find

1. the cartesian equation of the plane \({{\pi }_{2}}\).[3]
2. the vector equation of the line of intersection between the planes \({{\pi }_{1}}\) and \({{\pi }_{2}}\).[1]
3. the position vector of the foot of the perpendicular from the point \(B\left( -2,1,0 \right)\) to the plane \({{\pi }_{1}}\).[4]
4. the point of reflection of \(B\) in \({{\pi }_{1}}\).[2]