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Find the equation of the plane passing through the intersection of the planes 2x + 2y – 3z – 7 = 0 and 2x + 5y + 3z – 9 = 0 such that the intercepts made by the resulting plane on the x-axis and the z-axis are equal.

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Given planes are:

2x + 2y – 3z – 7 = 0 … (i)

and 2x + 5y + 3z – 9 = 0 … (ii)

Equation of the plane passing through the intersection of the planes (i) and (ii) is:

Which is the equation of required plane.

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