Video Transcript
Determine the intersection of the plane π·πΆπΆ dash π· dash and plane π΄π΅πΆπ· and plane π΄π·π· dash π΄ dash.
In this question, weβre looking for the vertex or edge at which the three planes intersect. Letβs first consider the plane π·πΆπΆ dash π· dash and the plane π΄π΅πΆπ·. Well, these two planes intersect along the edge πΆπ·. This is because they have a common edge πΆπ· belongs to the plane π·πΆπΆ dash and π· dash and also belongs to the plane π΄π΅πΆπ·.
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΅πΆπ· along the edge π΄π·. The plane π΄π·π· dash π΄ dash also intersects the plane π·πΆπΆ dash π· dash along the edge π·π· dash.
We were asked to determine the intersection of all three planes π·πΆπΆ dash π· dash intersects π΄π΅πΆπ· 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·πΆπΆ dash π· dash. It also exists in the plane π΄π΅πΆπ·. 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·.