4 In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.
(a) 2 x + 3y + 4 z - 12 = 0
Let the coordinates of the foot of perpendicular P from the origin to the plane be
Given a plane equation ,
Or,
The direction ratios of the normal of the plane are .
Therefore
So, now dividing both sides of the equation by we will obtain,
This equation is similar to where, are the directions cosines of normal to the plane and d is the distance of normal from the origin.
Then finding the coordinates of the foot of the perpendicular are given by .
The coordinates of the foot of the perpendicular are;
or