Subtraction and displacement

Subtraction and displacement: linear algebra practice

Practise vector subtraction with an explicit sense of direction. Questions move from signed component differences to coordinate displacements, relative motion and endpoint recovery. Each problem asks you to identify the reference point before calculating, making sign errors easier to detect and explain.

What you will practise

• Compute directed displacement as destination minus start
• Use subtraction to compare positions and velocities
• Recover endpoints and distinguish displacement from traveled distance

How to use this questionset

Prerequisites: Coordinate tuples, vector addition and scalar multiplication by minus one. 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.

A displacement is a vector with direction. A traveled distance is a nonnegative scalar and may depend on the route. Directed differences become the input to distance formulas, line equations and relative-position models. This microlearning belongs to Module 1, Vectors and Geometry, in the Complete Linear Algebra Course.