# Video: Finding the Intersection between Three Given Planes

Determine the intersection of the plane π·πΆπΆβ²π·β² and plane π΄π΅πΆπ· and plane π΄π·π·β²π΄β².

02:11

### Video Transcript

Determine the intersection of the plane π·πΆπΆ dash π· dash and plane π΄π΅πΆπ· and plane π΄π·π· dash π΄ dash.

In this question, weβre looking for the vertex or edge at which the three planes intersect. Letβs first consider the plane π·πΆπΆ dash π· dash and the plane π΄π΅πΆπ·. Well, these two planes intersect along the edge πΆπ·. This is because they have a common edge πΆπ· belongs to the plane π·πΆπΆ dash and π· dash and also belongs to the plane π΄π΅πΆπ·.

However, we also need to consider the plane π΄π·π· dash π΄ dash. We can see from the diagram that the plane π΄π·π· dash π΄ dash intersects π΄π΅πΆπ· along the edge π΄π·. The plane π΄π·π· dash π΄ dash also intersects the plane π·πΆπΆ dash π· dash along the edge π·π· dash.

We were asked to determine the intersection of all three planes π·πΆπΆ dash π· dash intersects π΄π΅πΆπ· intersects π΄π·π· dash and π΄ dash at the point π·. This is because π· is the only common vertex of all three planes. π· exists in the plane π·πΆπΆ dash π· dash. It also exists in the plane π΄π΅πΆπ·. And finally, π· is also a vertex of the plane π΄π·π· dash π΄ dash.

This means that the point of intersection is the vertex π·.

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