# Vector equations of lines in R3

This applet shows a line in ℝ^{3} and the vector form of its equation.

A vector equation for a line has the form **r** = **r**_{0} + t**v**, t ∈ ℝ where **r**_{0} is the position vector of a point on the line, and **v** is a vector parallel to the line.

You can click and drag **r**_{0} and **v** to adjust the line.

Try modifying both **r**_{0} and **v** in turn, to see what the resulting lines have in common.

By default you can only move the points horizontally (parallel to the xy-plane); if you wish to switch between moving the points horizontally or vertically, click on the point a second time.

If you select the “Constrain points to line” checkbox, the line will be locked in place, and **r**_{0} and **v** will only be able to be moved along the line. This allows you to see that the same line can have many possible vector equations.

Other resources:

Related applet: Vector equations of planes in R^{3}