Equation Of A Plane

The equation of a plane in three-dimensional space that cuts off equal intercepts of length 1 on the coordinate axes is determined by setting the intercept form of the plane equation:

Here, , , and are the intercepts on the , , and axes, respectively. For equal intercepts of unit length, we have .

Substituting these values into the intercept form gives:

Simplifying this, we obtain:

Therefore, the equation of the plane that cuts equal intercepts of unit length on each of the coordinate axes is .

The correct answer is the option: x+y+z=1.