mathvects

Velocity is a vector function example 2 fluid velocity

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online