# 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;

or              ..................(1)

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,

we get,

or

or

Then we will substitute the values of  in the equation (1), we get

or

This is the required equation of the plane.

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