ch12s3 - 12.3 The Dot Product Definition: Dot Product If...

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12.3 The Dot Product Definition: Dot Product If and , the dot product of and is the number given by . 123 ,, aaa = a bbb = b a b ab 11 2 2 33 ⋅= + + 1 cos cos cos θθ θ ⋅⋅ = = 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 =− − = ( 2)(1) ( 1)(4) (3)( 2) 2 4 6 12 ⋅=− +− + − = −−−= Example: Find the dot product of . ,2 =− =+ aik bi 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 this information as follows: Example: If 1 6, , 34 π === , find the dot product.
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ch12s3 - 12.3 The Dot Product Definition: Dot Product If...

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