Question

Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0. Also find the distance of the plane obtained above, from the origin.

Answer 1

The equation of a plane passing through the intersection of the given planes is

Since, (i) is perpendicular to x - y + z = 0

Putting the value of 1 in (i), we get

\(\Rightarrow\) x - z + 2 = 0, it is required plane.

Let d be the distance of this plane from origin.

[Note: The distance of the point \((\alpha, \beta, \gamma)\) to the plane ax + by + cz + d=0 is given by