91Ó°ÊÓ

The foot of the perpendicular from the origin to a plane is \((12,-4,-3)\). Find its equation.

Find the equation of the plane passing through the points: (i) \((8,-2,2),(2,1,-4),(2,4,-6)\) (ii) \((2,2,1),(2,3,2),(-1,3,0)\) (iii) \((2,3,4),(-3,5,1),(4,-1,2)\)

Find the equation of the plane bisecting the line joining the points \((2,3,-1)\) and \((-5,6,3)\) at right angles.

\(O A B C\) is a tetrahedron in which \(O A, O B\) and \(O C\) are mutually perpendicular. Prove that the perpendicular from \(O\) to the base \(A B C\) meets it at its orthocentre.