Three planes can intersect in a point

As important…. Your physics assignments can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result. Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form. Our experts will gladly share their knowledge and help you with programming projects. Analytic Geometry. Three planes can intersect in a number of different ways.

For each of the combinations below, find the single point of intersection if there is one. If there isn't, explain how the planes do intersect. Need a fast expert's response?

Place free inquiry. Calculate the price. Learn more about our help with Assignments: Analytic Geometry. Comments No comments. Be the first! Thank you! Your comments have been successfully added. The line can intersect a third plane in either a line or a single point prove this! It's easy to construct examples where each of these cases can happen. Sign up to join this community.

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CoolKid CoolKid 2, 2 2 gold badges 24 24 silver badges 43 43 bronze badges. Try to figure out what the intersection of each is geometrically.

Add a comment. Active Oldest Votes. And not intersect at all. If two planes intersect the intersection will be a line. Now if two or more of the planes coincide, there's one more case. Or two planes may be parallel and the third intersect both.

If the overlap, then they are both the same plane. Two distinct planes are either parallel and don't intersect at all or intersect at a line. Three planes can mutually intersect but not have all three intersect. The planes will then form a triangular "tube" and pairwise will intersect at three lines. This lines are parallel but don't all a same plane. Or three planes can, like the pages in the spine of a book, can intersect in one single line.

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