Line Through a Point (3D) Calculator
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
- Identify the point and direction components.
- Write the vector form of the line and substitute values.
- Write the parametric form and substitute values.
- Write the symmetric form when every direction component is nonzero.
Formula:
\(\vec{r} = \vec{r}_{0} + t\vec{d}\)
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