The point A has coordinates \((1,-2,4)\) and the plane \(\pi_1\) has the equation \(2x-y+2z=5\)
Find the exact shortest distance between \(A\) and \(\pi_1\).[2]
The plane \(\pi_2\) has equation \(x+3y-az=3\), where \(a\) is a constant.
Find the vector equation of line \(l\), which is the line of intersection of \(\pi_1\) and \(\pi_2\), in terms of \(a\).[4]
The plane \(\pi_3\) has equation \(bx-2y+4z=3\), where \(b\) is a constant.
Show that \((a-6)(b-4)=0\) if \(l\) is parallel to \(\pi_3\).[2]
State the conditions that \(a\) and \(b\) must follow for the three planes to form a triangular prism, where all the planes are non-parallel and they do not have any point in common. Justify your answer.[4]