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.

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}).

<a href="http://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>

Guelph Physics Tutorials: Vectors, (Department of Physics, University of Guelph, Guelph, 2006), <http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html>.

Guelph Physics Tutorials: Vectors. (2006, March 29). Retrieved August 2, 2015, from Department of Physics, University of Guelph: http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html

Department of Physics, University of Guelph. Guelph Physics Tutorials: Vectors. Guelph: Department of Physics, University of Guelph, March 29, 2006. http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html (accessed 2 August 2015).

Guelph Physics Tutorials: Vectors. Guelph: Department of Physics, University of Guelph, 2006. 29 Mar. 2006. 2 Aug. 2015 <http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html>.

@misc{
Title = {Guelph Physics Tutorials: Vectors},
Publisher = {Department of Physics, University of Guelph},
Volume = {2015},
Number = {2 August 2015},
Month = {March 29, 2006},
Year = {2006}
}

%T Guelph Physics Tutorials: Vectors %D March 29, 2006 %I Department of Physics, University of Guelph %C Guelph %U http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html %O text/html

%0 Electronic Source %D March 29, 2006 %T Guelph Physics Tutorials: Vectors %I Department of Physics, University of Guelph %V 2015 %N 2 August 2015 %8 March 29, 2006 %9 text/html %U http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html

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