11 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.
The equation of the plane through the intersection of the given two planes, and is given in Cartesian form as;
So, the direction ratios of (1) plane are which are .
Then, the plane in equation (1) is perpendicular to whose direction ratios are .
As planes are perpendicular then,
Then we will substitute the values of in the equation (1), we get
This is the required equation of the plane.
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