Q6 of 181 Page 1166

Find the equation of the plane which passes through the point (2, -3,7) and makes equal intercepts on the coordinate axes.

Equation of the plane making a, b & c intercepts with X, Y & Z axes respectively is



But, the plane makes equal intercepts on the co-ordinate axes


Therefore, a = b = c


Therefore the equation of the plane is



x + y + z = a


As plane passes through the point (2, -3, 7),


Substituting x = 2, y = -3 & z = 7


2 – 3 + 7 = a


Therefore, a = 6


Hence, required equation of plane is


x + y + z = 6


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