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A ‘black box’ approach to scalar and vector products

Published online by Cambridge University Press:  01 August 2016

Dylan Wiliam
Dylan Wiliam*
Affiliation:
Centre for Educational Studies, King's (Chelsea) College, University of London
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Extract

In the traditional approach to the teaching of vectors, the scalar product of two vectors u, v is usually defined to be

|u| . |v| . cos θ

where θ is defined to be the angle between the two vectors. In a similar way, the vector product of two vectors is defined to be a vector that makes a right handed triple with u and v, and whose length is given by

|u| . |v| . sin θ

From these definitions the familiar co-ordinate expressions for dot and cross products are derived.

Type
Research Article
Information
The Mathematical Gazette , Volume 70 , Issue 453 , October 1986 , pp. 197 - 200
Copyright
Copyright © The Mathematical Association 1986

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