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EAS208_L20_030411

EAS208_L20_030411 - EAS 208 Spring 2011 Cross Product...

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EAS 208 – Spring 2011 Cross Product Definition: The cross product is an operation between two vectors in three-dimensional Euclidean space. The cross product of vector and vector , denoted as u v × uv , is defined as: ˆ if , 0, 0, and sin if 0, or 0 θ θπ ≠≠ ⎧⋅⋅ ×= = == = e where is the interior angle between u and , and is a unit vector normal to the plane of u and , directed such that the vectors , , form a right-handed system. Note, that the result of the cross product v ˆ e v u v ˆ e × is a vector. Figure 1 Cross Product of vector u and vector v Properties: ( ) − × vu (anticommutativity) () ( ) aa × uv uv (associativity) ( ) ( ) +×=× +× uv w uw vw (distributivity) 1

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Geometric Significance: The magnitude of the cross product × uv is equal to the area of the u , parallelogram as illustrated in Figure (2) (

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EAS208_L20_030411 - EAS 208 Spring 2011 Cross Product...

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