Intersection of three planes

Find the common point of the three planes given by their normals and constant terms. State whether it does not exist or the solution is a line.

Step-by-step solution

Solve the system of three linear equations.
If the determinant of the normals is not 0, there is a single point.
If the determinant is 0, the planes are dependent: they may share a line or have no common point.
Check the result by substituting the point into all three equations.

Result: they meet at point P(5, 14, 11).

Three planes can leave a point, a line, a plane (if two coincide) or nothing. Do not assume there is always a point.