Line Through a Point (3D) Calculator

Published on: August 30, 2026
Final Answer: Free Full Steps: Pro

This Line Through a Point with a Direction Vector Calculator helps you find the equation of a line in three-dimensional space from a given point and direction vector. Use the point as the starting position and the direction vector to describe how the line moves in the x-, y-, and z-directions. This gives the line in vector form and parametric form. It is a simple way to check answers, understand the method clearly, and practise 3D coordinate geometry step by step.

Step-by-step method

  1. Identify the point and direction components.
  2. Write the vector form of the line and substitute values.
  3. Write the parametric form and substitute values.
  4. Write the symmetric form when every direction component is nonzero.

Formula:

\(\vec{r} = \vec{r}_{0} + t\vec{d}\)