Video: Finding the Intersection between Two Given Planes

In the following figure, determine the intersection of plane 𝐴𝐷𝐴′ and plane 𝐡𝐷𝐡′.

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Video Transcript

In the following figure, determine the intersection of plane 𝐴𝐷𝐴 prime and plane 𝐡𝐷𝐡 prime.

First, let’s identify plane 𝐴𝐷𝐴 prime. 𝐴𝐷𝐴 prime, we know that a plane is a flat two-dimensional surface that extends infinitely. And that means that plane 𝐴𝐷𝐴 prime does not just include this triangular piece. It includes these spaces and continues to extend in all directions.

Let’s go ahead and identify the plane space that includes 𝐡𝐷𝐡 prime. 𝐡𝐷𝐡 prime, here is the shape created by 𝐡𝐷𝐡 prime. And here is a representation of the plane that 𝐡𝐷𝐡 prime lies in. Here’s a reduced sketch of these two planes.

We remember that the intersection of two planes is a line. We need to identify the line that is the intersection of these two planes. Line 𝐢𝐢 prime is the intersection of these two planes. What we mean by that is at every point along the line 𝐢𝐢 prime is both plane 𝐴𝐷𝐴 prime and plane 𝐡𝐷𝐡 prime.

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