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Earn +20 ptsQ: How many planes can contain a given line in space?
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How many planes contain a given line in space?
Given a line, there are an infinite number of different planes that it lies in.
How many planes can contain two given points?
If 2 points determine a line, then a line contains infinitely many planes.
How many planes can contain a line and a point on the line?
Anything that contains the line must contain every point on the line, so "a point on the line" doesn't give us any more information. You're just asking how many planes can contain the line. Now imagine setting a wood panel down on a tight-rope. How many different ways can it set there before it falls off ? A lot, right ? An infinite number of planes can all contain your line. (And all of its points.)
How many planes can intersect a line at a given point?
an infinite number; no limit
Can two planes in three-dimensional space intersect at one point?
No, they intersect at a line.
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