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# Velocity is a vector function example 2 fluid velocity

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Unformatted text preview: is a vector function. ~ Example 2: Fluid velocity is a vector function and one example is V = ^ ^ ; y^ + 0k xi j B. The Dot and Cross Product There are two types of multiplication of vectors one result is a scalar(i.e. a number) and the other is a vector. ~~ The Dot Product: A B =j A jj B j cos The resultant of the dot product is a scalar. 2 y A = (1,3,2) (1,0,0) x (0,0,2) z Figure 2: Sketch of a vector in three-dimensional space as in example 1. A θ B Figure 3: Sketch of the geometry associated with the dot product. 3 ~ ~ ~~ Example 3: Given: A = (1 0 0), B = (1 2 0). Find: A B . Solution: The dot product is obtained by multiplying the magnitude of each vector together and multplying by the cosine of the angle between them: ~~ p A B = 1 5 p15 = 1 Alternatively, we could multiply each component of each vector together and add to get the same answer: ~~ A B = A1B1 + A2B2 + A3B3 ~~ ~~ Note that A B = B A. ~~ The Cross Product: A B The easiest way to calculate the cross product is to view it like a determinant: ^^k ij^ ~ B = A1 A2 A3 = (A2B3;A3B2)^;(A1B3;A3B1)^+(A1B2;A2B1)k ~ ^ A i j B1 B2 B3 Note that the result of the cross product is a vector. The magnitude of the r...
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## This note was uploaded on 02/17/2013 for the course AME 331 taught by Professor Zohar during the Spring '08 term at Arizona.

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