Vector Equation of a Line

Vector Equation of a Line

A line passing through a point with position vector $$\vec a$$ and having direction vector $$\vec d$$ is:

$$\vec r=\vec a+\lambda\vec d$$

Terminology

- $$\vec r$$: Position vector of a variable point on the line.

- $$\vec a$$: Position vector of a fixed point on the line.

- $$\vec d$$: Direction vector.

- $$\lambda$$: Scalar parameter.

Usage

- Standard vector form of a straight line in 3D.