Equations of a Line in 3D

A line in 3D can be represented in various forms, each useful for different purposes.

Vector Form

Cartesian Form

Example: Equation of a Line

Symmetric Form

Two-Point Form

Example: Two-Point Form

Angle Between Two Lines

Practice Problems

1. Write the equation of a line through with direction ratios .
2. Find the equation of a line through and .
3. Find the angle between lines with direction ratios and .
4. Convert to vector form.