Q: Can two distinct points both exist on two distinct lines?

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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.

points, lines and planes. points are always represented by a dot lines has extend in both direction and planes extend in all direction. this is true !

One.

They are both vertical lines.

If both lines have the same slope and the same y-intercept, they're the same line. So, infinite intersection points, I guess.

Related questions

No. Two points determine one line, and only one.

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.

If there are no common points but both lines lie n the same plane they are considered "coplanar points"

Points do not extend, lines do.

The intersection of two distinct planes is a line. The set of common points in the line lies in both planes.

Yes it does have both female and male

the answer is 1

One.

points, lines and planes. points are always represented by a dot lines has extend in both direction and planes extend in all direction. this is true !

Yes

One.

No. The circular shape makes it impossible to have parallel lines just as you cannot have parallel lines in a circle that both reach the length of the diameter of the said circle.