A total of 33 types of planes can be laid out on a Cartisean Space in 3D divided into 5 Categories. Following are they:

- Planes that a perpendicular to a coordinate axis. There are 3 types of such planes.
S.No Equation Intercepts **Explanation**1. \( x=C \) =C*x Intercept*=Undefined*y Intercept*=Undefined*z Intercept*These planes are perpendicular to *X axis*(and consequently parallel to*Y and Z axis*). The plane \(x=0\) is the*YZ plane*.2. \( y=C \) =Undefined*x Intercept*=C*y Intercept*=Undefined*z Intercept*These planes are perpendicular to *Y axis*(and consequently parallel to*X and Z axis*). The line \(y=0\) is the*XZ plane*.3. \( z=C \) =Undefined*x Intercept*=Undefined*y Intercept*=C*z Intercept*These planes are perpendicular to *Z axis*(and consequently parallel to*X and Y axis*). The line \(z=0\) is the*XY plane*. - Planes that a pass through origin but do not contain any coordinate axis (and hence their normals are not perpendicular to any coordinate axis) . There are 4 types of such planes.
**S.No****Equation****Intercepts****Explanation**1. \( Ax+By+Cz=0 \) *OR*

\(-Ax-By-Cz=0\)=0*x Intercept*=0*y Intercept*=0*z Intercept*These planes have normals aligned in 1st and 7th octant 2. \( Ax+By-Cz=0 \) *OR*

\(-Ax-By+Cz=0\)=0*x Intercept*=0*y Intercept*=0*z Intercept*These planes have normals aligned in 2nd and 8th octant 3. \( Ax-By+Cz=0 \) *OR*

\(-Ax+By-Cz=0\)=0*x Intercept*=0*y Intercept*=0*z Intercept*These planes have normals aligned in 3rd and 5th octant 4. \( -Ax+By+Cz=0 \) *OR*

\(Ax-By-Cz=0\)=0*x Intercept*=0*y Intercept*=0*z Intercept*These planes have normals aligned in 4th and 6th octant - Planes that a pass through origin but and contain a coordinate axis (and hence their normals perpendicular to that coordinate axis) . There are 6 types of such planes.
**S.No****Equation****Intercepts****Explanation**1. \( Ax+By=0 \) *OR*

\(-Ax-By=0 \)=0*x Intercept*=0*y Intercept*=Undefined*z Intercept*These planes contain *Z axis*and their normals are perpendicular to it2. \( Ax-By=0 \) *OR*

\(-Ax+By=0 \)=0*x Intercept*=0*y Intercept*=Undefined*z Intercept*These planes contain *Z axis*and their normals are perpendicular to it3. \( By+Cz=0 \) *OR*

\(-By-Cz=0 \)=Undefined*x Intercept*=0*y Intercept*=0*z Intercept*These planes contain *X axis*and their normals are perpendicular to it4. \( By-Cz=0 \) *OR*

\(-By+Cz=0 \)=Undefined*x Intercept*=0*y Intercept*=0*z Intercept*These planes contain *X axis*and their normals are perpendicular to it5. \( Ax+Cz=0 \) *OR*

\(-Ax-Cz=0 \)=0*x Intercept*=Undefined*y Intercept*=0*z Intercept*These planes contain *Y axis*and their normals are perpendicular to it6. \( Ax-Cz=0 \) *OR*

\(-Ax+Cz=0 \)=0*x Intercept*=Undefined*y Intercept*=0*z Intercept*These planes contain *Y axis*and their normals are perpendicular to it - Planes that make distinct intercepts on coordinate axes. There are 8 types of such planes, 1 for each octant.
**S.No****Equation****Intercepts****Explanation**1. \( Ax+By+Cz+D=0 \) *OR*

\(-Ax-By-Cz-D=0\)=\(\frac{-D}{A}\)*x Intercept*=\(\frac{-D}{B}\)*y Intercept*=\(\frac{-D}{C}\)*z Intercept*All Intercepts are negative. Plane is in 7th Octant 2. \( Ax+By+Cz-D=0 \) *OR*

\(-Ax-By-Cz+D=0\)=\(\frac{D}{A}\)*x Intercept*=\(\frac{D}{B}\)*y Intercept*=\(\frac{D}{C}\)*z Intercept*All Intercepts are positive. Plane is in 1st Octant 3. \( Ax+By-Cz+D=0 \) *OR*

\(-Ax-By+Cz-D=0\)=\(\frac{-D}{A}\)*x Intercept*=\(\frac{-D}{B}\)*y Intercept*=\(\frac{D}{C}\)*z Intercept*Plane is in 8th Octant 4. \( Ax-By+Cz+D=0 \) *OR*

\(-Ax+By-Cz-D=0\)=\(\frac{-D}{A}\)*x Intercept*=\(\frac{D}{B}\)*y Intercept*=\(\frac{-D}{C}\)*z Intercept*Plane is in 3rd Octant 5. \( -Ax+By+Cz+D=0 \) *OR*

\(Ax-By-Cz-D=0\)=\(\frac{D}{A}\)*x Intercept*=\(\frac{-D}{B}\)*y Intercept*=\(\frac{-D}{C}\)*z Intercept*Plane is in 6th Octant 6. \( Ax+By-Cz-D=0 \) *OR*

\(-Ax-By+Cz+D=0\)=\(\frac{D}{A}\)*x Intercept*=\(\frac{D}{B}\)*y Intercept*=\(\frac{-D}{C}\)*z Intercept*Plane is in 2nd Octant 7. \( Ax-By+Cz-D=0 \) *OR*

\(-Ax+By-Cz+D=0\)=\(\frac{D}{A}\)*x Intercept*=\(\frac{-D}{B}\)*y Intercept*=\(\frac{D}{C}\)*z Intercept*Plane is in 5th Octant 8. \( -Ax+By+Cz-D=0 \) *OR*

\(Ax-By-Cz+D=0\)=\(\frac{-D}{A}\)*x Intercept*=\(\frac{D}{B}\)*y Intercept*=\(\frac{D}{C}\)*z Intercept*Plane is in 4th Octant - Planes that are parallel to a coordinate axis (and hence their normal are perpendicular to that axis). There are 12 types of such planes.
**S.No****Equation****Intercepts****Explanation**1. \( Ax+By+D=0 \) *OR*

\(-Ax-By-D=0\)=\(\frac{-D}{A}\)*x Intercept*=\(\frac{-D}{B}\)*y Intercept*=Undefined*z Intercept*These planes are parallel to *Z axis*and their normals are perpendicular to it2. \( Ax+By-D=0 \) *OR*

\(-Ax-By+D=0\)=\(\frac{D}{A}\)*x Intercept*=\(\frac{D}{B}\)*y Intercept*=Undefined*z Intercept*These planes are parallel to *Z axis*and their normals are perpendicular to it3. \( Ax-By+D=0 \) *OR*

\(-Ax+By-D=0\)=\(\frac{-D}{A}\)*x Intercept*=\(\frac{D}{B}\)*y Intercept*=Undefined*z Intercept*These planes are parallel to *Z axis*and their normals are perpendicular to it4. \( -Ax+By+D=0 \) *OR*

\(Ax-By-D=0\)=\(\frac{D}{A}\)*x Intercept*=\(\frac{-D}{B}\)*y Intercept*=Undefined*z Intercept*These planes are parallel to *Z axis*and their normals are perpendicular to it5. \( By+Cz+D=0 \) *OR*

\(-By-Cz-D=0\)=Undefined*x Intercept*=\(\frac{-D}{B}\)*y Intercept*=\(\frac{-D}{C}\)*z Intercept*These planes are parallel to *X axis*and their normals are perpendicular to it6. \( By+Cz-D=0 \) *OR*

\(-By-Cz+D=0\)=Undefined*x Intercept*=\(\frac{D}{B}\)*y Intercept*=\(\frac{D}{C}\)*z Intercept*These planes are parallel to *X axis*and their normals are perpendicular to it7. \( By-Cz+D=0 \) *OR*

\(-By+Cz-D=0\)=Undefined*x Intercept*=\(\frac{-D}{B}\)*y Intercept*=\(\frac{D}{C}\)*z Intercept*These planes are parallel to *X axis*and their normals are perpendicular to it8. \( -By+Cz+D=0 \) *OR*

\(By-Cz-D=0\)=Undefined*x Intercept*=\(\frac{D}{B}\)*y Intercept*=\(\frac{-D}{C}\)*z Intercept*These planes are parallel to *X axis*and their normals are perpendicular to it9. \( Ax+Cz+D=0 \) *OR*

\(-Ax-Cz-D=0\)=\(\frac{-D}{A}\)*x Intercept*=Undefined*y Intercept*=\(\frac{-D}{C}\)*z Intercept*These planes are parallel to *Y axis*and their normals are perpendicular to it10. \( Ax+Cz-D=0 \) *OR*

\(-Ax-Cz+D=0\)=\(\frac{D}{A}\)*x Intercept*=Undefined*y Intercept*=\(\frac{D}{C}\)*z Intercept*These planes are parallel to *Y axis*and their normals are perpendicular to it11. \( Ax-Cz+D=0 \) *OR*

\(-Ax+Cz-D=0\)=\(\frac{-D}{A}\)*x Intercept*=Undefined*y Intercept*=\(\frac{D}{C}\)*z Intercept*These planes are parallel to *Y axis*and their normals are perpendicular to it12. \( -Ax+Cz+D=0 \) *OR*

\(Ax-Cz-D=0\)=\(\frac{D}{A}\)*x Intercept*=Undefined*y Intercept*=\(\frac{-D}{C}\)*z Intercept*These planes are parallel to *Y axis*and their normals are perpendicular to it