Video: Finding the Intersection between Three Planes

What is the intersection of planes 𝑀𝐴𝐡, 𝑀𝐡𝐢 and 𝑀𝐴𝐢?

01:19

Video Transcript

What is the intersection of planes 𝑀𝐴𝐡, 𝑀𝐡𝐢, and 𝑀𝐴𝐢?

If we firstly consider the planes 𝑀𝐴𝐡 and 𝑀𝐡𝐢, it is clear from the diagram that the two planes intersect along the edge or line 𝑀𝐡. This is because 𝑀 and 𝐡 are common vertices of the two planes.

Adding in the third plane 𝑀𝐴𝐢, we can see that this intersects the plane 𝑀𝐴𝐡 along the edge or line 𝑀𝐴. In a similar way, the plane 𝑀𝐴𝐢 intersects the plane 𝑀𝐡𝐢 along the edge or line 𝑀𝐢.

However, we were asked for the intersection of all three planes: 𝑀𝐴𝐡, 𝑀𝐡𝐢, and 𝑀𝐴𝐢. Well, it is clear from the diagram that the only point or vertex, where all three planes intersect is point 𝑀 β€” vertex 𝑀. This is because the only common vertex of the three planes 𝑀𝐴𝐡, 𝑀𝐡𝐢, and 𝑀𝐴𝐢 is vertex 𝑀.

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