Position vectors and tuples

Position vectors and tuples: linear algebra practice

Practise moving between position vectors and ordered tuples in a specified coordinate system. Begin with endpoints measured from the origin, then interpret zero and negative coordinates, higher-dimensional lists and changes in the coordinate description. The emphasis is on what each entry means, not on memorizing a diagram.

What you will practise

• Translate between a point and its position vector
• Read ordered coordinates in two, three and higher dimensions
• Diagnose coordinate-order and origin errors

How to use this questionset

Prerequisites: Free vectors, Cartesian axes, signed numbers and elementary equations. 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.

Every tuple uses the coordinate order stated in the question. A physical drawing is not needed for a vector with more than three components. This representation will support componentwise arithmetic and later coordinate systems. This microlearning belongs to Module 1, Vectors and Geometry, in the Complete Linear Algebra Course.