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How many pairs of vertical angles are formed by 3 coplanar lines intersecting at one point?
Eight.
How many pairs of vertical angles are formed by 5 coplanar lines intersecting at one point?
20....or maybe 18
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.
What is different of collinear point from non collinear point and coplanar point from non coplanar point?
Three or more points are collinear if they are all in the same straight line. They are non collinear if at least one of them is not on the same line as the rest. Four or more points are coplanar if they are all in the same plane. They are non coplanar if at least one of them is not on the same plane as the rest.
Two lines lie in one plane if and only if the lines are parallel?
Two lines are coplanar iff they are parallel OR intersect.
What different relationships can occur between two coplanar lines?
-- They can be parallel, with no points in common, or -- They can intersect in exactly one point.
How many pairs of vertical angles are formed by 3 coplanar lines intersecting at one point?
Eight.
Do non-coplanar forces can be concurrent forces?
¢The forces, which meet at one point, but their lines of action do not lie on the same plane, are known as non-coplanar concurrent forces.
How many pairs of vertical angles are formed by 5 coplanar lines intersecting at one point?
20....or maybe 18
If two lines are coplanar then that means they much touch?
Either not at all, or at exactly one point. There's no other possibility.
Lines that have one point in common?
Intersecting lines. If they have only one point in common, then they are also non-parallel.
What are 2 or more lines located on one plane called?
Coplanar lines.
Parallel lines are defined as lines that have only one point in common?
No, parallel lines never intersect, so they do not have any points in common. Intersecting lines have one common point.
What line is coplanar and meet at a point?
One line cannot be coplanar, and there is nothing for it to meet.
What is lines that have exactly one point in common?
Food lines
Lines that have exactly one point in common?
intersecting lines
What are lines that exactly one point in common?
Intersecting lines
