What Is 3D Distance?
The 3D distance between two points is the length of the straight line segment connecting them through three-dimensional space. It generalizes the 2D distance formula by adding a third dimension: the differences in x, y, and z coordinates are treated as the edges of a rectangular box, and the distance is the box's space diagonal.
This measure is fundamental whenever positions are described with three coordinates, such as in navigation, physics, and computer graphics.
Formula
d = √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²)
Applications
- Measuring the distance between two aircraft or vessels using 3D coordinates
- Computing distances between atoms or objects in molecular modeling
- Determining how far apart two points are in 3D CAD and 3D printing layouts
- Calculating object positions in video game engines and 3D graphics
- Finding drift or separation between drones and other moving vehicles
Sources
- Stewart, J. (2015). Calculus: Early Transcendentals (8th ed.). Cengage Learning.
- Thomas, G. B., Weir, M. D., & Hass, J. (2014). Thomas' Calculus (13th ed.). Pearson.