Video: Finding the Intersection between Two Given Planes

Video Transcript

What is the intersection of the planes 𝑀𝐴𝐵 and 𝑀𝐵𝐶?

To answer this question, let’s first recall the geometric postulate regarding the intersection of two planes. It tells us that if two planes intersect, then the intersection is a line. So if the planes 𝑀𝐴𝐵 and 𝑀𝐵𝐶 do intersect, then the type of intersection we’re looking for is a line.

Let’s now add some shading to the diagram so that we can see these planes more clearly. The plane 𝑀𝐴𝐵 is now shaded in pink and the plane 𝑀𝐵𝐶 is now shaded in orange. By doing this, we can see the line that is common to both planes. It’s the line 𝑀𝐵.

Hopefully, you’ll find this fairly intuitive as the points 𝑀 and 𝐵 are common to both planes. So our answer to the problem is that the intersection of the planes 𝑀𝐴𝐵 and 𝑀𝐵𝐶 is the line 𝑀𝐵.