Question

None of the three planes intersect: none of the three planes intersect 2. the three planes intersect in one line: the three planes intersect in one line 3. the three planes intersect in one point: the three planes intersect in one point 4. two planes do not intersect. the third plane intersects the other two.: two planes do not intersect. the third plane intersects the other two. 5. exactly two planes intersect. the third plane does not intersect the other two.: exactly two planes intersect. the third plane does not intersect the other two.

Answer 1

Three planes in space can be parallel, mutually perpendicular, or intersect in various combinations. Parallel planes do not intersect, and mutually perpendicular planes intersect at a single point of concurrency.

Step-by-step explanation:

When considering three planes in a three-dimensional space, there are several ways in which they can be arranged with respect to one another:

• Scenario a: If all three planes are parallel to each other, there is no point or line where they intersect. They simply extend infinitely without ever meeting.
• Scenario b: When three planes are mutually perpendicular, they intersect at a single point, which is where all three planes meet. This is known as the point of concurrency.
• Other scenarios involve combinations such as two planes being parallel and the third intersecting them, or two planes intersecting along a line while the third does not intersect either of them.

Understanding the positional relationships between planes is fundamental in geometry and can be visualized with the aid of diagrams or three-dimensional models. This knowledge is applicable in fields like engineering, architecture, and physics.

Answer 2

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