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(vx, vy) = (cvx, cvy).
<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>
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).
%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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