Given two unique parallel planes, what are the possible solutions when a third plane with an unknown orientation is introduced? Consider how all three planes might intersect and the points shared by all three.

A. Infinite solutions on a plane
B. Infinite solutions along a line
C. One unique solution
D. No solution

Question

25-06-2024
Mathematics

Answered

Given two unique parallel planes, what are the possible solutions when a third plane with an unknown orientation is introduced? Consider how all three planes might intersect and the points shared by all three.

A. Infinite solutions on a plane
B. Infinite solutions along a line
C. One unique solution
D. No solution

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-25T15:47:50-04:00

Final answer:

When adding a third plane to two unique parallel planes, the solution set can have infinite solutions, form a line, have a unique solution, or have no solution.

Explanation:

When introducing a third plane to two unique parallel planes, the possibilities for the solution set can vary:

infinite solutions on a plane: if the third plane is parallel to the other two
infinite solutions along a line: when the third plane intersects both of the given planes
one unique solution: if the third plane is exactly the same as one of the given planes
no solution: in cases where the orientation of the third plane does not allow for intersection with the other two planes

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