Finding Points on Plane / Intercepts of Plane

The Standard Form of equation of plane is given as

\(Ax + By + Cz + D=0\)

The following are the steps to find the Points on the Plane.

  1. If all three co-efficients \(A\), \(B\) and \(C\) are not zero, then any arbitrary values can be put for any two coordinates to find the third coordinate.
  2. If any one of the co-efficient is missing, then the plane is either parallel to that coordinate (when \(D\neq0\)) or the plane contains that coordinate (when \(D=0\)) and the coordinate can have any value for the plane. Any arbitrary value can be put for any one of the two coordinates present to find the corresponding third coordinate.
  3. If any two of the co-efficients are missing, then the corresponding coordinates can have any value for the plane. The third coordinate will be a constant and the plane is perpendicular to that coordinate axis.
The following are the steps to find the Intercepts of the Plane.
  1. If \(D=0\) then the plane passes through the origin and does not have any other intercepts.
  2. If \(D\neq0\) then intercept of any axis can be found by setting the other two coordinate values to 0 and then evaluating the non-zero coordinate axis.