Line Through Two Points (3D) Calculator

Published on: April 19, 2026
Final Answer: Free • Full Steps: Pro

This Line Through Two Points (3D) Calculator helps you find the equation of a line in three-dimensional space that passes through two given points. First use the two points to find the direction vector, then substitute that vector and one point into the line equation. 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 components.
  2. Compute the direction vector P₂ − P₁.
  3. Write the vector form r = r₁ + t(P₂ − P₁) and substitute values.
  4. Write the parametric form (and symmetric form if applicable).

Formula:

\(\vec{r} = \vec{r}_{1} + t\left(P_{2} - P_{1}\right)\)