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