Question
If 4x + 4y – kz = 0 is the equation of the plane through the origin that contains a line 
then find the value of k.
Solution
The equation of plane is 4x + 4y – kz = 0 ...(1)
It passes through the origin (0, 0, 0).
The equation of line is
...(2)
The line has direction ratios 2, 3, 4.
Since the line (2) lies in the plane (1)
∴ normal to the plane with direction ratios 4, 4, – k is perpendicular to the line (1).
∴ (2) (4) + (3) (4) + (4) (– k) = 0
∴ 8 + 12 – 4 k = 0 ⇒ 4 k = 20 ⇒ k = 5.
