Find the vector equation of the plane passing through the intersection of the planes and = – 5 and the point (1, 1, 1).

The equation of the plane passing through the intersection of



[


…… (1)


[].


…… (2)


The required plane also passes through the point (1,1,1)


Substituting x = 1, y = 1, z = 1 in eq. (2),we have,


= (6 – 5k)


1 + 2k + 1 + 3k + 1 + 4k = 6 – 5k


3 + 9k = 6 – 5k


14k = 3


k =


Substituting the value k = in equation (1),We have,




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