two points

In Geometry, we define a point as a location and no size. A line is defined as something that extends infinitely in either direction but has no width and is one dimensional while a plane extends infinitely in two dimensions. A point has no size; it only has a location.

A point is an exact position or location on a plane surface. It is important to understand that a point is not a thing, but a place. We indicate the position of a point by placing a dot with a pencil. This dot may have a diameter of, say, 0.2mm, but a point has no size.

If the A, B and C are three collinear points then AB + BC = AC or AB = AC – BC or BC = AC – AB. If the area of triangle is zero then the points are called collinear points. If three points (x1, y1), (x2, y2) and (x3, y3) are collinear then [x1(y2 – y3) + x2( y3 – y1)+ x3(y1 – y2)] = 0.

What are the names of three collinear points? Points L, J, and K are collinear.

Three or more points that lie on the same line are collinear points . Example : The points A , B and C lie on the line m . There is no line that goes through all three points A , B and D .

: not collinear: a : not lying or acting in the same straight line noncollinear forces. b : not having a straight line in common noncollinear planes.

Three or more points , , ., are said to be collinear if they lie on a single straight line. . A line on which points lie, especially if it is related to a geometric figure such as a triangle, is sometimes called an axis. Two points are trivially collinear since two points determine a line.

Collinear points are points all in one line and non collinear points are points that are not on one line. Below points A, F and B are collinear and points G and H are non collinear.

Non-collinear points: These points, like points X, Y, and Z in the above figure, don’t all lie on the same line. Coplanar points: A group of points that lie in the same plane are coplanar. Any two or three points are always coplanar. Four or more points might or might not be coplanar.

Coplanar points are three or more points which all lie in the same plane. Any set of three points in space is coplanar. A set of four points may be coplanar or may be not coplanar.

Points that are located on a plane are coplanar If any three points determine a plane then additional points can be checked for coplanarity by measuring the distance of the points from the plane, if the distance is 0 then the point is coplanar.

A. B. C. D. Points P, M, F, And C Are Coplanar Points F, D, P, And N Are Coplanar.

Coplanar means “lying on the same plane”. Points are coplanar, if they are all on the same plane, which is a two- dimensional surface. Any three points are coplanar (i.e there is some plane all three of them lie on), but with more than three points, there is the possibility that they are not coplanar.

A necessary and sufficient condition for four points A(a ),B(b ),C(c ),D(d ) to be coplanar is that, there exist four scalars x,y,z,t not all zero such that xa +yb +zc +td =0 and x+y+z+t=0.

2 Answers. Take any three of the points and determine the equation of the plane. If the three points you chose do happen to lie on a single line then you are done- any fourth point will determine a plane that all four points lie on.

Slope of AB = (6 – 4)/ (4 – 2) = 1, Slope of BC = (8 – 6)/ (6 – 4) = 1, and. Slope of AC = (8 – 4) /(6 – 2) = 1. Since slopes of any two pairs out of three pairs of points are same, this proves that A, B and C are collinear points.

Similarly, a finite number of vectors are said to be non-coplanar if they do not lie on the same plane or on the parallel planes. In this case we cannot draw a single plane parallel to all of them. Theorem: If and be any three non-zero and non-coplanar space vectors such that then x = y = z = 0.

Coplanar vectors are the vectors which lie on the same plane, in a three-dimensional space. We can always find in a plane any two random vectors, which are coplanar.

According to the Triangle Law of vector addition, a minimum of three vectors are needed to get zero resultant. So we can say that a minimum of 3 coplanar vectors is required to represent the same physical quantity having different magnitudes that can be added to give zero resultant.

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. The angle between two intersecting planes is known as the dihedral angle.