Hypothetically, an infinite number of planes.
We humans develop contrived measurements, such as 360 degrees in a circle, but that does not mean there are only 360 possible angles; even subdividing as we do with 60 minutes in a degree, and 60 seconds in a minute, there is no hypothetical smallest fraction of an angle. You could have one-billionth of a degree of an angle to differentiate one plane from another passing through the same point, or one-quadrillionth, or one-googoleth, or one googole-plexeth, ad-infinitum (-eth).
Only one if they are non-collinear. An infinite number if they are collinear.
four.
There are 56 such planes.
No, perpendicular planes intercept at only one point. Parallel planes do not intersect at all.
I would say that there are an infinite number of planes that can pass through a pair of skew lines. In order to find the equation of a plane, all you need is three points. take two points off of one line and one point off of the other line and you should be able to derive the equation of a plane. Since the number of points on a line is infinite, an infinite number of planes can be derived.
infinite
Infinitely many.
Infinitely many.
Only one if they are non-collinear. An infinite number if they are collinear.
1
A sphere has an infinite number of planes of symmetry. The plane must include the center of the sphere, but it can tilt at any angle. The question is the same as asking "How many planes can be drawn through one point ?" The answer is: An infinite number. And as long as the point is the center of the sphere, each plane is a plane of symmetry of the sphere.
four.
There are 56 such planes.
No, perpendicular planes intercept at only one point. Parallel planes do not intersect at all.
3
one
Infinitely many planes.