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Unformatted text preview: is the scalar v w = x 1 x 2 + y 1 y 2 + z 1 z 2 . The denition of the dot product exhibits a number of algebraic properties, which we leave to you to verify (Exercise 3 ): Proposition 1.4.2. The dot product has the following algebraic properties: 1. It is commutative : v w = w v 2. It distributes over vector sums 11 : u ( v + w ) = u v + u w 3. it respects scalar multiples : ( r v ) w = r ( v w ) = v ( r w ) . Also, the geometric interpretation of the dot product given by Equation ( 1.17 ) yields a number of geometric properties: 10 Also the scalar product , direct product , or inner product 11 In this formula, u is an arbitrary vector, not necessarily of unit length....
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 Fall '08
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 Calculus, Factoring, Vectors

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