Distance Between Line and Point Calculator
Shortest Distance: - units
Projection Point: -
Parameter t: -
Understanding Line-Point Distance
What is Line-Point Distance?
The shortest distance between a line and a point is the length of the perpendicular line from the point to the line.
d = ||(Q - P₀) × v|| / ||v||
Projection Point = P₀ + tv
where:
- P₀ is a point on the line
- v is the direction vector
- Q is the external point
- t = (Q - P₀)·v / (v·v)
- × denotes cross product
- · denotes dot product
Vector Analysis Concepts
- Vector Operations:
- Cross Product: Direction perpendicular
- Dot Product: Scalar projection
- Vector Normalization
- Parametric Equations
- Geometric Properties:
- Perpendicularity
- Vector Projection
- Line Parameterization
- Distance Minimization
Applications and Extensions
Computer Graphics
Ray-object intersection
Robotics
Path planning
CAD Systems
Design optimization
Physics
Particle trajectories