Arrows and free vectors

Arrows and free vectors: linear algebra practice

Build a geometric understanding of free vectors by comparing arrows drawn at different locations. This questionset connects verbal directions, coordinate displacements and translated diagrams. You will distinguish the information that identifies a vector from the incidental position of its drawing, then apply that distinction to endpoint problems and explanations of common errors.

What you will practise

• Recognize equal free vectors despite different starting points
• Compare length and direction without confusing parallelism with equality
• Recover endpoints and diagnose transformations of an arrow

How to use this questionset

Prerequisites: Basic Cartesian coordinates, signed numbers and subtraction. The questions progress from direct interpretation to application and reasoning. Work out an answer before comparing the choices; for multi-select questions, evaluate every statement independently. Worked explanations show the reasoning and address relevant misconceptions, so an incorrect attempt can guide your next review.

All geometric comparisons use a fixed coordinate frame and scale; no unseen diagram or measurement is required. These ideas prepare you for position vectors, tip-to-tail addition and displacement calculations. This microlearning belongs to Module 1, Vectors and Geometry, in the Complete Linear Algebra Course.