Video: Finding the Intersection between Three Planes

What is the intersection of planes 𝑀𝐴𝐵, 𝑀𝐵𝐶 and 𝑀𝐴𝐶?

01:19

Video Transcript

What is the intersection of planes 𝑀𝐴𝐵, 𝑀𝐵𝐶, and 𝑀𝐴𝐶?

If we firstly consider the planes 𝑀𝐴𝐵 and 𝑀𝐵𝐶, it is clear from the diagram that the two planes intersect along the edge or line 𝑀𝐵. This is because 𝑀 and 𝐵 are common vertices of the two planes.

Adding in the third plane 𝑀𝐴𝐶, we can see that this intersects the plane 𝑀𝐴𝐵 along the edge or line 𝑀𝐴. In a similar way, the plane 𝑀𝐴𝐶 intersects the plane 𝑀𝐵𝐶 along the edge or line 𝑀𝐶.

However, we were asked for the intersection of all three planes: 𝑀𝐴𝐵, 𝑀𝐵𝐶, and 𝑀𝐴𝐶. Well, it is clear from the diagram that the only point or vertex, where all three planes intersect is point 𝑀 — vertex 𝑀. This is because the only common vertex of the three planes 𝑀𝐴𝐵, 𝑀𝐵𝐶, and 𝑀𝐴𝐶 is vertex 𝑀.

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