Are parallel lines in space coplanar sometimes?

Are parallel lines in space coplanar?

Parallel lines will be co-planar.

If two distinct lines do not intersect are they parallel?

If they are coplanar in a Euclidean space, then yes. If they are not coplanar or not in Euclidean space, then not necessarily.

If two lines are not coplanar then they are neither intersecting nor parallel?

CorrectParallel lines as well as intersecting lines must be coplanar (in Euclidean geometry not quite sure about hyperbolic geometry...).Lines in space which neither are coplanar nor intersecting are called "skew"

Where do two lines intersect?

In Euclidean space, they could intersect along their whole lengths (in the lines are identical), at a point if they are coplanar and not parallel, or nowhere if they are parallel or skew.

When are skew lines coplanar?

Never! Coplanar means that the two lines lie in the same two-dimensional plane. The only way that two lines do not intersect in two-dimensional space is if they are parallel. And by definition, skew lines are not allowed to be parallel, either.So essentially there is no such thing as skew lines that only occupy two dimensions. Skew lines must be in three dimensions or higher in order to (1) not intersect and (2) not be parallel with each other.

How many non coplanar line determine a space?

3 non-coplanar (pairwise) lines for 3 dimensional space.

When there is a transversal of two lines the three lines are coplanar?

Normally, yes. A transversal contemplates crossing two (normally parallel) lines in conversations about two dimensional space and the relationship of certain angles. If you are talking about three dimensions, all bets are off. Two skewed lines in three dimensional space could would have a line that connects them but none of them would be coplanar.

What are two lines that do not lie in the same place called?

Two lines that do not lie in the same place are called non-coplanar lines. This means that the lines do not intersect and are not parallel to each other in three-dimensional space.

What are coplanar angles?

mama mo * * * * * An angle is formed when 2 lines meet at a point: the vertex. Two lines which meet in this way always define a plane. Coplanar angle are two or more angles which are all in the same plane. In 3-dimensional space, it is easy to find angles which are not coplanar. For example, in a cuboid room, the angle formed by the lines where the floor meets two adjacent walls, and where the ceiling meets the same two walls are not coplanar: the angles lie in parallel planes. The same first angle and the angle formed where the ceiling meets another pair of walls are neither coplanar nor in parallel planes: they are in skew planes.

What are lines that go on foever and never cross?

In 2-dimensional space they must be parallel. In 3-d space they be parallel or skew lines I believe.

Are lines with three dimensions which do not intersect are not parallel?

Non-intersecting lines in 3-D space may be parallel but need not be.

What are non-coplanar lines?

In Euclidean Geometry, two non-coplanar lines are two lines in 3-dimensional space for which no single plane contains allpoints in both lines. For any two lines in three dimensional space, there is always at least one plane that contains all points in one line and at least one point in the other line. But there is not always (in fact it's quite rare) that any plane will contain all points in both lines. When it happens, there is only one such plane for any two distinct lines. Note that, any two lines in 3-dimensional space that intersect each other mustbe coplanar. Also, any two lines in 3-dimensional space that are parallel to each other must also be coplanar. So, in order to be non-coplanar, two lines in 3-dimensional space must a) not intersect each other at any point, and b) not be parallel to each other. (As it turns out, this dual condition is not only necessary, but sufficient for non-coplanarity.) Also note that, as a test for coplanarity of two lines, you need only test two points on each line, for a total of four points, because all points on a single line are, by definition, on the same plane. In fact, all you really have to do is test a single point on one line against three other points (one on the same line and two on the other line), because, by definition, any three points in 3-dimensional space are on the same plane. For example, consider any two distinct points on line m (A and B), and any two distinct points on line l (C and D). Points A and B are obviously coplanar because they are colinear (in fact, they are coplanar in the infinite number of planes that contain this line). Point C on line l is also coplanar with points A and B, because by definition, any 3 non-colinear points in 3-dimensional space define a plane (however, if point C is not on line m, the number of planes that contain all three points is immediately reduced from infinity to one). So the coplanarity test for the first three points is trivial - they are coplanar no matter what. However, it is not at all certain that point D will be on the same plane as points A, B, and C. In fact, for any two random lines in 3-dimensional space, the probability that the four points (two on each line) are coplanar is inifinitesimally small. But, if the fourth point, the one not used to define the plane, is nevertheless coplanar with the three points that define the plane, then lines l and m are coplanar. Note that, though I specified that points A and B on line m must be distinct, and that points C and D on line l must be distinct, I did not specify that C and D must both be distinct from both A and B. That is because, if, for example, A and C are the same (not distinct) point, then, obviously, lines m and l intersect, at point A, which is the same as point C. If this is the case, then the question of whether D is on the same plane as A, B, and C is trivial, because you really only have 3 distinct points, and any three distinct points alwaysshare a plane. That is why intersecting lines (lines that share a single point) are always coplanar. But you're asking about non-coplanar lines. So, basically, if any point on either of the two lines is not coplanar with the other three points (one on the same line and two on the other line), then the lines are non-coplanar.

Are parallel lines in space coplanar sometimes?

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