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chap12sec3 - 12.3 The Dot Product Definition Dot Product =...

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12.3 The Dot Product Definition: Dot Product If  1 2 3 , , a a a = a  and  1 2 3 , , b b b = b , the  dot product  of  a  and  b  is the number  a b  given by  1 1 2 2 3 3 a b a b a b = + + a b . Note that the dot product is not a vector; it is a scalar. It is sometimes called the scalar (inner) product. Don't confuse this with  scalar multiplication. You can also find the dot product of two-dimensional vectors the same way. Look at the  properties on page 797.   The TI-86 calculator will perform the dot product operation.  Access the vector menu. Example: Find the dot product of  2, 1,3 , 1,4, 2 = - - = - a b ( 2)(1) ( 1)(4) (3)( 2) 2 4 6 12 = - + - + - = - - - = - a b Example: Find the dot product of  , 2 = - = + a i k b i j . There is a geometric interpretation of the dot product that can be given in terms of the angle between the vectors. Look at  Figure 1 on page 797 and  Theorem 3.  This theorem gives us a way to find the angle between two vectors. We can summarize 
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