Question
The foot of the perpendicular drawn from the origin to the plane is (4, 3, 2). Find the equation of the plane. 
Solution
The equation of plane through M (4, 3, 2) is
a (x – 4) + b (Y–3) + c (z – 2) = 0 ...(1)
The direction-ratios of the line through the points O (0, 0. 0) and M (4, 3, 2) are
4 - 0, 3-0, 2-0 i.e. 4, 3, 2
∴ the line OM with direction-ratios 4, 3, 2 is normal to the plane (1)
∴ equation (1) of plane becomes
4 (X – 4) + 3 (y – 3) + 2 (z – 2) = 0 
or 4x – 16 + 3 Y – 9 + 2z – 4 = 0 or 4x + 3y + 2z – 29 = 0
