Answer to Question #103689 in Analytic Geometry for deepak

Question

The set of all the points (x, y,z) satisfying the equation x−z = z−y represents a

line. Check whether true or false.

Answer 1

$x-z=z-y\\ x+y-2z=0$

The canonical equation of the plane is ax+by+cz+d=0.

This means that the equation represents a plane, not a line.

Answer: false.