Position Vectors

Introduction

• Earlier we defined the difference between vectors and coordinates:
  • Coordinates:
    • These represent fixed locations in space.
  • Vectors:
    • These represent fixed change.
• Position vectors are vectors that represent fixed locations in space.
• They represent the vector needed to get from the origin to a specific location.
• For example, the vector needed to get from the origin (0,0) to (1, 2) is:
• Position vectors differ from coordinates in that they have the ability to be transformed:
  • While it is possible to translate a coordinate, it doesn't make much sense to scale or rotate it.
  • Because position vectors are relative to the origin, they can be rotated and scaled, as well as translated.