Correct option is A. x + y + z = 1
We know, that the general equation of a plane is given by,
Ax + By + Cz + D = 0, where D ≠ 0……… (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, \(A=-\cfrac{D}a,\) \(B = -\cfrac{D}b\) and \(C=-\cfrac{D}c\) and the plane makes intercepts at (a, 0, 0), (0, b, 0) and (0, 0, c) with the x - , y - and z - axes respectively.
Here, a = b = c = 1. 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.
