- The plane \(\Pi\) passes through the points
$$A ( - 1 , - 1,1 ) , B ( 4,2,1 ) \text { and } C ( 2,1,0 )$$
- Find a vector equation of the line perpendicular to \(\Pi\) which passes through the point \(D ( 1,2,3 )\).
- Find the volume of the tetrahedron \(A B C D\).
- Obtain the equation of \(\Pi\) in the form r.n \(= p\).
The perpendicular from \(D\) to the plane \(\Pi\) meets \(\Pi\) at the point \(E\).
- Find the coordinates of \(E\).
- Show that \(D E = \frac { 11 \sqrt { 35 } } { 35 }\).
The point \(D ^ { \prime }\) is the reflection of \(D\) in \(\Pi\).
- Find the coordinates of \(D ^ { \prime }\).
(3)
[0pt]
[P6 June 2002 Qn 7]