Question
In the following cases, find the coordinates of the foot of the perpendicular
drawn from the origin.
2x + 3y + 4z – 12 = 0
Solution
The equation of given plane is
2 x + 3 y + 4 z – 12 = 0 ...(1)
Dividing both sides by 
∴ direction cosines of the normal OP are 
where O is origin and P(x1,y1, z1) is foot of perpendicular.
Direction ratios of OP are x1 – 0, y1 – 0, – 0 i.e. x1, y1, z1.
Since direction cosines and direction ratios of a line are proportional.
Since P lies on plane (1)
