# What is a parametric equation of a line

## 3 Parametric Equations of a Line in 3D Space The parametric equations of a line L in 3D space are given by x =x0 +ta,, y =y0 +tb, z =z0 +tc where )(x0, y0,z0 is a point passing through the line and v = < a, b, c > is a vector that the line is parallel to.

Examples demonstrating how to calculate parametrizations of a line. Or, if we write x=(x,y,z), we could write the parametric equation in component form as

This is analogous to a curve generalizing a straight line. There are several more precise definitions, depending on the context and the mathematical tools that are used for the study.

Thanks for the A2A. I haven't done vectors in a long time, so there may be some mistakes. First, the line of intersection lies on both planes. Therefore, it shall be  The vector equation of the line is a parametric equation of the form $\mathbf{r}=\mathbf{a}+\lambda \mathbf{d}$. Experiment with the co…
We develop the vector equation of the straight line expressed in coordinates: and by separating the coordinates we obtain: These are the parametric equations  Lines: Two points determine a line, and so does a point and a vector.. Example 1: Find parametric equations for the line passing through the point P(4,−1,3)  Lines: Two points determine a line, and so does a point and a vector.. Example 1: Find parametric equations for the line passing through the point P(4,−1,3)  You can sometimes recover the x-y equation of a parametric curve by eliminating t from the parametric Find parametric equations for the line through $(3, -6)$