Question Video: Intersection between Planes | Nagwa Question Video: Intersection between Planes | Nagwa

# Question Video: Intersection between Planes Mathematics • Second Year of Secondary School

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What is the intersection of the plane through π΄π΅π΅β²π΄β² and the plane through π΅πΆπΆβ²π΅β²?

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### Video Transcript

What is the intersection of the plane through π΄π΅π΅ dash π΄ dash and the plane through π΅πΆπΆ dash π΅ dash?

Letβs first consider the plane π΄π΅π΅ dash π΄ dash as shown in the diagram. Well this plane has four edges π΄π΅, π΅π΅ dash, π΅ dash π΄ dash, and π΄ dash π΄ and four vertices: π΄, π΅, π΅ dash, and π΄ dash.

Now letβs consider the second plane, π΅πΆπΆ dash π΅ dash. This plane also has four edges π΅πΆ, πΆπΆ dash, πΆ dash π΅ dash, and π΅ dash π΅. It also has four vertices: π΅, πΆ, πΆ dash, and π΅ dash.

Where do these two planes intersect? Do they intersect at a vertex or point or do they intersect at an edge? Well it is clear from the diagram that the two planes intersect at π΅π΅ dash.

Therefore, the intersection of the plane through π΄π΅π΅ dash π΄ dash and the plane through π΅πΆπΆ dash π΅ dash is the line or edge π΅π΅ dash. You will notice that when looking at the original two planes, the two vertices that appear in both of them are π΅ and π΅ dash.

This means that the planes must intersect at π΅ and π΅ dash. We could write this as the intersection of π΄π΅π΅ dash π΄ dash and π΅πΆπΆ dash π΅ dash is π΅π΅ dash.

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