Question
Find the distance of the point (2, 3, 4) from the plane 3x + 2y + 2z + 5 = 0, measured parallel to the line 
Solution
The equation of given plane is
3x + 2y + 2z + 5 = 0 ...(1)
The equations of the line through P (2, 3, 4) parallel to the line
Any point on it is Q (3r + 2, 6 r + 3, 2r + 4)
Let it lie on plane (1)
∴ 3 (3 r + 2) + 2 (6 r + 3) + 2 (2 r + 4) + 5 = 0
or 9r + 6 + 12r + 6 + 4r + 8 + 5 = 0
or 25 r= – 25 or r = – 1
∴ point Q is ( – 3 + 2, – 6 + 3, –2 + 4) i.e. (–1,–3, 2)
