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.

1.

For intersecting planes, the intersection is a line.

2.

Parallel planes.

3.

Coincident planes.

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