Question
Find the coordinates of the foot of perpendicular from the point (2, 2, 7) to the plane 3 x – y – z = 7. Also find the length of perpendicular.
Solution
The equation of plane is
3x – y – z = 7 ...(1)
Direction ratios of the normal to the plane are 3, – 1, – 1.
Let M be the foot of perpendicular from P (2, 2, 7) to the plane.
Now MP is a straight line which passes through P (2, 2, 7) and has direction ratios as 3, – 1, – 1.
its equations are 
Any point on line is M (3 r + 2, – r + 2, – r + 7)
∵ M lies on plane (1)
∵ 3 (3 r + 2) – (– r + 2) – (– r + 7) = 7
∴ 9r + 6 + r – 2 + r – 7 = 7
