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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 points may a line contain?

A line, ray, or line segment contains an infinite number of points.


Given a line and a point on that line how many different planes contain both of them?

1


Given a line and a point not on that line how many different planes contain both of them?

1


How many planes can contain a given line in space?

There's no limit to the number of them. A more cool and sexy way to say the same thing might be: "An infinite number."


How many planes can contain two given points?

If 2 points determine a line, then a line contains infinitely many planes.


Does every line have an infinite number of lines perpendicular to the given line?

Yes. There can be a line perpendicular to the given line at every point on it, and you know how many different points there are on it ...


In general how many planes are there which contain any number of given points?

There are no planes containing any number of given points. Two points not the same define a line. Three points not in a line define a plane. For four or more points to lie in the same plane, three can be arbitrary but not on the same line, but the fourth (and so on) points must lie in that same plane.


How many planes can intersect a line at a given point?

an infinite number; no limit


How many nonzero numbers are a given distance from zero on a number line?

It's 6


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 contain one specific line?

An infinite number of planes. Picture a line and now picture planes going in every direction through the line,