The Standard Form of Equation of Plane is given as
\(Ax + By + Cz + D=0\)
The following gives the Steps to Find the Points on the Plane as given by the equation above
If all three Co-efficients \(A\), \(B\) and \(C\) are Not Zero, then Any Arbitrary Values can be put for Coordinate Variables Corresponding to Any 2 Coordinate Axes to find the Value of Coordinate Variable Corresponding to 3rd Coordinate Axis.
If Any One of the Co-efficient is Missing, then the Coordinate Variable corresponding to the Missing Co-efficient can have Any Value for the Plane.
Any Arbitrary Value can be put for Any One of the 2 Coordinate Varibles present to find the Value of remaining Coordinate Variable.
If Any 2 of the Co-efficients are Missing, then the Corresponding Coordinates Variables can have Any Value for the Plane.
The Value of Coordinate Variable Corresponding to Co-efficient that is present is Constant as given by the equation.
The Intercepts of a Plane are Points where the Plane Intersects the Coordinate Axes. The following are the Steps to Find the Intercepts of the Plane on the Coordinate Axes.
If \(D=0\) then the Plane Passes through the Origin and Does Not Form Intercepts on Any of the Coordnate Axes.
If \(D\neq0\) then the Intercept of the Plane on Any Coordinate Axis can be found by Setting the Coordinate Variables corresponding to Other 2 Coordinate Axes to 0 and then evaluating the Coordinate Variable Corresponding to that Coordinate Axis.