Parallel lines would always lie in the same plane. They would need to be skew lines.
They're either parallel lines or skew lines.
-- An infinite number of different planes can intersect the same line. -- The same line can lie in an infinite number of different planes. -- An infinite number of different lines can intersect the same plane.
Skew lines are lines that lie on separate planes. and do not intercept parallel lines that are sometimes on the same plane, but don't intersect
skew lines
Noncoplanar lines cannot intersect because they exist in different planes and do not share a common point. However, they can be skew lines, which means they are neither parallel nor intersecting. In three-dimensional space, two lines are only able to intersect if they lie in the same plane. Therefore, it is geometrically impossible for two noncoplanar lines to intersect.
They're either parallel lines or skew lines.
-- An infinite number of different planes can intersect the same line. -- The same line can lie in an infinite number of different planes. -- An infinite number of different lines can intersect the same plane.
Skew lines are lines that lie on separate planes. and do not intercept parallel lines that are sometimes on the same plane, but don't intersect
skew lines
skew lines
true * * * * * No, false. Any two straight lines that intersect define a plane in which both those lines lie.
Not necessarily. Points may lie in different planes.
Noncoplanar lines cannot intersect because they exist in different planes and do not share a common point. However, they can be skew lines, which means they are neither parallel nor intersecting. In three-dimensional space, two lines are only able to intersect if they lie in the same plane. Therefore, it is geometrically impossible for two noncoplanar lines to intersect.
Skew lines.
Two lines may or may not lie in the same plane, depending on their relationship. If the lines are parallel or intersecting, they exist in the same plane. However, if the lines are skew, meaning they do not intersect and are not parallel, they lie in different planes. Thus, whether two lines lie in the same plane is contingent on their geometric arrangement.
Skew lines in 3 dimensional geometry, do not lie in the same plane, and will not intersect. Think of an overpass 'crossing' a freeway. From an aerial view they appear to intersect, but one is above the other (in different planes). They do not touch each other.
Parallel lines. they never intersect and lie on the same plane.parallel lines