Vector Projection Calculator

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Projection Result

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Understanding Vector Projection

What is Vector Projection?

Vector projection is a fundamental concept in linear algebra that helps us find how much of one vector extends in the direction of another vector. The resulting projection is always parallel to the vector being projected onto.

Applications

Vector projections are widely used in:

  • Physics - For analyzing forces and motion
  • Computer Graphics - In 3D rendering and shadow calculations
  • Robotics - For motion planning and control
  • Machine Learning - In various algorithms and computations

Formula Used

The vector projection formula is:

projba = (a·b / |b|²) × b

Where:

  • a·b is the dot product of vectors a and b
  • |b| is the magnitude of vector b
  • b is the vector being projected onto