Question Video: Finding the Intersection of Two Planes | Nagwa Question Video: Finding the Intersection of Two Planes | Nagwa

Question Video: Finding the Intersection of Two Planes Mathematics • Second Year of Secondary School

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π and π are planes that intersect at line πΏ. π΅ is a point on plane π and πΆ is a point on plane π. Determine the intersection of plane π with plane π΄π΅πΆ.

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Video Transcript

π and π are planes that intersect at line πΏ. π΅ is a point on plane π, and πΆ is a point on plane π. Determine the intersection of plane π with plane π΄π΅πΆ.

In our figure, we can see line πΏ is the intersections of plane π and π. We want the intersection of plane π with plane π΄π΅πΆ. Letβs first identify plane π. We can see that the plane π includes the points π΄ and πΆ. And if weβre interested in plane π΄π΅πΆ, we recognize that the points π΄ and π΅ are located along the same plane, plane π, and the points πΆ and π΄ are both located in the plane π. This tells us that the point π΄ is located in plane π and in plane π.

Because the points π΄, π΅, and πΆ are noncolinear, they can form exactly one plane. To see plane π΄π΅πΆ, first, weβll connect a line through points π΄ and π΅ and another line through the points π΄, πΆ. From there, we can add an additional line that goes through point πΆ. By connecting these lines, we have some idea of how this plane would look.

At this point, we should start to see that the plane π΄π΅πΆ is slicing through the plane π. And this slicing is happening along the line that goes through the points π΄ and πΆ. Plane π contains the line π΄πΆ, as does plane π΄π΅πΆ, which makes the intersection of plane π and plane π΄π΅πΆ the line π΄πΆ.

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