This post categorized under Vector and posted on September 28th, 2019.

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A line is defined as the set of alligned points on the plane with a point P and a directional vector . If P(x 1 y 1) is a point on the line and the vector has the same direction as then equals multiplied by a scalar unit A tutorial on how to find a vector from one point to another and hence find the vector equation of a straight line through two points. This was requested via twitter mathormaths. In this vector we derive the vector and parametic equations for a line in 3 dimensions. We then do an easy example of finding the equations of a line.

The vector equation of a line is r a tb. In this equation a represents the vector position of some point that lies on the line b represents a vector that gives the direction of the line r represents the vector of any general point on the line and t represents how much of b is needed to get from a to the position vector. When we try to specify a line in three dimensions (or in n dimensions) however things get more involved. It can be done without vectors but vectors provide a really clear and quick way into the problem. This is called the vector form of the equation of a line. The only part of this equation that is not known is the (t). Notice that (tvec v) will be a vector that lies along the line and it tells us how far from the original point that we should move.

In mathematics a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables. If P(x 1 y 1) is a point on the line and the vector has the same direction as then Examples. A line pvectores through point A (1 3) and has a directional vector with components (2 5). If a is vector OA and b is vector OB then the equation of the line can be written (). A ray starting at point A is described by limiting . One ray is obtained if 0 and the opposite ray comes from 0. Equations of Lines and Planes Lines in Three Dimensions A line is determined by a point and a direction. Thus to find an equation representing a line in three dimensions choose a point P_0 on the line and a non-zero vector v parallel to the line.