Kollinær

Kollinær is a term used in geometry to describe points that lie on the same straight line. If three or more points are collinear, it means that a single straight line can be drawn that passes through all of them. Conversely, if points do not lie on the same line, they are called non-collinear.

The concept of collinearity is fundamental in various areas of mathematics and its applications. For instance, in coordinate geometry, points are collinear if the slope between any pair of points is the same. If points A, B, and C are collinear, the slope of the line segment AB will be equal to the slope of the line segment BC, and also equal to the slope of the line segment AC.

Determining collinearity can be done using several methods. In a two-dimensional Cartesian coordinate system, given three points (x1, y1), (x2, y2), and (x3, y3), they are collinear if the area of the triangle formed by them is zero. This can be calculated using the determinant formula: 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|. If this expression equals zero, the points are collinear.

In three-dimensional space, collinearity can be checked by verifying if the vectors formed by pairs of points are parallel. If points A, B, and C are collinear, then the vector AB is a scalar multiple of the vector BC. This means their corresponding components are proportional. The concept is also important in fields like physics, surveying, and computer graphics, where the alignment of objects or measurements is crucial.