3 or more Planes are said to form a family if either

- The planes are collinear i.e. they pass through a common line of intersection
- The planes are parallel to each other

\(A_1x + B_1y + C_1z + D=0\)

AND

\(A_2x + B_2y + C_2z + D=0\)

The equation of any plane that is either parallel to these 2 planes or is collinear with these 2 planes is given as

\(A_1x + B_1y + C_1z + D + k(A_2x + B_2y + C_2z + D) = 0\)

The value of the variable \(k\) can be found out when some additional input is given. Following are some additional inputs that are generally given

- The point through which the resulting plane passes
- The plane/axis to which the resulting plane is parallel or perpendicular