We know, that the general equation of a plane is given by,
Ax + By + Cz + D=0, where ……… (1)
Here, A, B, C are the coordinates of a normal vector to the plane, while (x, y, z) are the co - ordinates of any point through which the plane passes.
Again, we know the intercept form of plane which is given by,
Where, and and the plane makes intercepts at (a, 0, 0), (0, b, 0) and (0, 0, c) with the x - , y - and z - axes respectively.
Putting, the value of a, b, c in equation (2), we are getting,
x + y + z=1
Hence, the equation of the plane which cuts equal intercepts of unit length on the coordinate axes is, x + y + z=1.
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