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Unformatted text preview: 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...
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