# What Is Vector Equation Of Line

This post categorized under Vector and posted on July 5th, 2018.

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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.The vector equation of a line is an equation that is satisfied by the vector that has its head at a point of the line. This vector is not in general a vector that lies on the line unless the line pgraphices through the origin (that is the common starting point of all vectors).Thus the line has vector equation r-123t30-1. Hence the parametric equations of the line are x-13t y2 and z3-t. It is important to note that the equation of a line in three dimensions is not unique. Choosing a different point and a multiple of the vector will yield a different equation.

Matrix - Vector Equations. A system of linear equations can always be expressed in a matrix form. For example the system . 4x 2y 4 2x - 3y -3. is equivagraphict to the matrix equation. Algebraically both of these express the same thing. The matrix version of the equation has its own geometric interpretation.position vector direction vector vector addition scalar multiple vector equation line Now we do know how to come up with the equation of a line using a lot of different methods for example you could be given a point and a graphic and use the point graphic formula to come up with the equation of a line.Jun 13 2008 Write down a vector equation for the line joining the two points (231) and (315). What is the graphicgth of this line I have already worked out the vector equation which is 14i - 7j - 7k.Status ResolvedAnswers 8

Example 1 Write down the equation of the line that pgraphices through the points and . Write down all three forms of the equation of the line. Solution. To do this we need the vector that will be parallel to the line. This can be any vector as long as its parallel to the line. In general wont lie on the line itself.