Video: Finding the Intersection between Two Given Planes

What is the intersection of the planes ๐‘€๐ด๐ต and ๐‘€๐ต๐ถ?

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Video Transcript

What is the intersection of the planes ๐‘€๐ด๐ต and ๐‘€๐ต๐ถ?

To answer this question, letโ€™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 ๐‘€๐ด๐ต and ๐‘€๐ต๐ถ do intersect, then the type of intersection weโ€™re looking for is a line.

Letโ€™s now add some shading to the diagram so that we can see these planes more clearly. The plane ๐‘€๐ด๐ต is now shaded in pink and the plane ๐‘€๐ต๐ถ is now shaded in orange. By doing this, we can see the line that is common to both planes. Itโ€™s the line ๐‘€๐ต.

Hopefully, youโ€™ll find this fairly intuitive as the points ๐‘€ and ๐ต are common to both planes. So our answer to the problem is that the intersection of the planes ๐‘€๐ด๐ต and ๐‘€๐ต๐ถ is the line ๐‘€๐ต.

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