ScalarProductandWork - SCALAR(DOT PRODUCT Before we define...

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1 SCALAR (DOT) PRODUCT Before we define work in physics we need to first define the scalar (dot) product between two vectors. The reason for this is because we will define work in terms of the scalar (dot) product between the force vector and displacement vector. cos (Scalar Product) AB θ •= AB (Commutative Law) (Distributive Law) AB B •A A•(B+C)=A•B+A•C A B q Note that the scalar product is a scalar quantity and not a vector quantity! Ex. 1 A B A B A B = AB cos 90 = 0 Ex. A parallel to B A B A B =ABcos0=AB Ex. A antiparallel to B A B A B = AB cos 180 = - AB Dot Product Between Unit Vectors ˆˆ ˆˆ ˆˆ cos0 1 0 ˆ ˆ 1 0 ˆ ˆ 0 ii i i i j jj ik kk jk =
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2 222 2 Given two vectors and : ˆ ˆˆ ˆ : (Scalar Product Between Two Vectors) Ex. (Magnitude of Vector ) xy z xx yy zz xyz Ai A j Ak Bi B j Bk Then AB AAAA A =++ •= + + •= + + = =• A B AA A WORK DONE BY A CONSTANT FORCE
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ScalarProductandWork - SCALAR(DOT PRODUCT Before we define...

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