Given two planes:

Form a system with the equations of the planes and calculate the ranks.

r = rank of the coefficient matrix.

r'= rank of the augmented matrix.

The relationship between the two planes can be described as follows:

Position r r'  
Intersecting 2 2
Parallel 1 2
Coincident 1 1

State the relationship between the planes.


For intersecting planes, the intersection is a line.


Parallel planes.


Coincident planes.

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