Question
Find the equation of the plane passing through the origin and parallel to the vectors 
Solution
The equation of any plane through (0, 0, 0) is
A (x – 0) + B (y – 0) + C (z – 0) = 0
or Ax + By + C z = 0 ...(1)
Since it is parallel to the vectors 
∴ normal to the plane with direction ratios A, B, C is perpendicular to the lines with direction ratios 1, 1,–1 and 3, 0,–1.
∴ A + B – C = 0 ...(2)
and 3A + 0B – C = 0 ...(3)
Solving (2) and (3), we get,
or 
Putting these values of A, B, C in (1), we get,
kx + 2ky + 3kz = 0
or x + 2 y + 3z = 0
which is required equation of plane.
