---
tag: 0JW13B48YP
kind: concept
name: Vector projection
aliases: [orthogonal-projection-onto-a-vector]
msc: [51N20]
sources:
  - url: https://en.wikipedia.org/wiki/Vector_projection
    locator: lead section
same_as:
  wikidata: Q2734388
  wikipedia: Vector projection
---

## Summary

The vector projection of a vector $a$ onto a nonzero vector $b$ is the multiple of $b$ that is nearest to $a$. It is the shadow of $a$ on the line of $b$, under light that falls perpendicular to that line.