Guelph Physics Tutorials: Vectors

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published by the Department of Physics, University of Guelph

This page offers a straightforward tutorial on the fundamentals of vector operations. It is an illustrated guide to vector subtraction/addition, vector resolution, and multiplication of two vectors. It could serve as textbook supplementation or as content support for science teachers.

https://www.physics.uoguelph.ca/vector-tutorial

Subjects	Levels	Resource Types
General Physics - Measurement/Units = Coordinates = Scaling Mathematical Tools - Vector Algebra Other Sciences - Mathematics	- High School - Lower Undergraduate	- Instructional Material = Problem/Problem Set = Tutorial

Intended Users	Formats	Ratings
- Learners - Educators	- text/html	Currently 0.0/5 Want to rate this material? Login here!

Access Rights:: Free access
Restriction:: © 2006 Department of Physics, University of Guelph
Keywords:: TPT Websights, coordinates, direction, magnitude, measurement, notation, resolving a vector, scale, tutorial, vector addition, vector components, vector resolution, vectors
Record Cloner:: Metadata instance created July 31, 2008 by Christopher Bares
Record Updated:: February 23, 2025 by Lyle Barbato
Last Update when Cataloged:: March 29, 2006
Other Collections:: The Physics Front

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Common Core State Standards for Mathematics Alignments

High School — Number and Quantity (9-12)

Vector and Matrix Quantities (9-12)

N-VM.1 (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
N-VM.2 (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
N-VM.3 (+) Solve problems involving velocity and other quantities that can be represented by vectors.
N-VM.4.a Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
N-VM.4.b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
N-VM.4.c Understand vector subtraction v — w as v + (—w), where —w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.
N-VM.5.a Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v_x, v_y) = (cv_x, cv_y).

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<a href="https://www.compadre.org/portal/items/detail.cfm?ID=7754">Department of Physics, University of Guelph. Guelph Physics Tutorials: Vectors. Guelph: Department of Physics, University of Guelph, March 29, 2006.</a>

AIP Format

(Department of Physics, University of Guelph, Guelph, 2006), WWW Document, (https://www.physics.uoguelph.ca/vector-tutorial).

AJP/PRST-PER

Guelph Physics Tutorials: Vectors (Department of Physics, University of Guelph, Guelph, 2006), <https://www.physics.uoguelph.ca/vector-tutorial>.

APA Format

Guelph Physics Tutorials: Vectors. (2006, March 29). Retrieved May 1, 2025, from Department of Physics, University of Guelph: https://www.physics.uoguelph.ca/vector-tutorial

Chicago Format

Department of Physics, University of Guelph. Guelph Physics Tutorials: Vectors. Guelph: Department of Physics, University of Guelph, March 29, 2006. https://www.physics.uoguelph.ca/vector-tutorial (accessed 1 May 2025).

MLA Format

Guelph Physics Tutorials: Vectors. Guelph: Department of Physics, University of Guelph, 2006. 29 Mar. 2006. 1 May 2025 <https://www.physics.uoguelph.ca/vector-tutorial>.

BibTeX Export Format

@misc{ Title = {Guelph Physics Tutorials: Vectors}, Publisher = {Department of Physics, University of Guelph}, Volume = {2025}, Number = {1 May 2025}, Month = {March 29, 2006}, Year = {2006} }

Refer Export Format

%T Guelph Physics Tutorials: Vectors %D March 29, 2006 %I Department of Physics, University of Guelph %C Guelph %U https://www.physics.uoguelph.ca/vector-tutorial %O text/html

EndNote Export Format

%0 Electronic Source %D March 29, 2006 %T Guelph Physics Tutorials: Vectors %I Department of Physics, University of Guelph %V 2025 %N 1 May 2025 %8 March 29, 2006 %9 text/html %U https://www.physics.uoguelph.ca/vector-tutorial

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