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.
The following are the steps to find the Intercepts of the Plane.
- 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.
- 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.
- 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.
- If \(D=0\) then the plane passes through the origin and does not have any other intercepts.
- 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.