Vector Projection Calculator | Free Online Math Tools

Vector Projection Calculator

Calculate the projection of vector a onto vector b with our easy-to-use calculator.

Enter Vector Components

Vector a

Vector b

Result:

⟨ 0, 0, 0 ⟩

Understanding Vector Projection

Vector projection is a fundamental concept in linear algebra and geometry. It calculates the vector component of one vector that is parallel to another vector.

Key Concepts

  • The projection formula is: proj_b(a) = (a·b/||b||²)b
  • The result is always parallel to vector b
  • The magnitude of the projection represents the "shadow" length

Applications

Vector projection is used in many fields, including:

  • Physics: Force decomposition and motion analysis
  • Computer Graphics: Shadow calculations and ray tracing
  • Engineering: Structural analysis and signal processing