Vector projection of A onto B: proj_B(A) = (A·B/|B|²)B. Scalar projection: comp_B(A) = A·B/|B|. Rejection: A − proj_B(A) is perpendicular to B. The projection decomposes A into components parallel and perpendicular to B.
How to Use
Enter two vectors:
- A: Vector to project
- B: Direction to project onto
- Output: Projection and rejection
Formulas
- Scalar: A·B / |B|
- Vector: (A·B / |B|²) × B
- Rejection: A − proj_B(A)
Applications
Work in physics (F·d), shadow casting, decomposing forces, least-squares approximation, and signal processing.
Step-by-Step Instructions
- 1Enter vector A.
- 2Enter vector B.
- 3View scalar projection.
- 4View vector projection.
- 5Check rejection vector.