Vector Multiplication - pgccphy.net

Vector Simpson, of Physical Sciences and EngineeringPrince George s Community CollegeSeptember 18, 2010 IntroductionWhen dealing with scalars, there is only one definition of Multiplication : you multiply one scalar by anotherscalar, giving a scalar result according to the usual laws of arithmetic:a bDc. But with vectors, therearethreedifferent kinds of Multiplication : one kind gives a scalar result, another gives a Vector result, andanother gives a tensor result. Here we ll summarize the various types of Vector Multiplication and show howto compute each in terms of the rectangular components of the begin, let s represent vectors ascolumn vectors that is,3 1matrices. We ll define the vectorsAandBas the column vectorsAD0@AxAyAz1 AIBD0@BxByBz1A(1)We ll now see how the three types of Vector Multiplication are defined in terms of these column vectors andthe rules of matrix ProductThefirst type of Vector Multiplication is called thedot product.

Vector Multiplication D.G. Simpson,Ph.D. DepartmentofPhysicalSciencesandEngineering Prince George’s Community College September18,2010 Introduction

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  Vector, Multiplication, Vector multiplication

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