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notes001 (7) - The Cross Product Outline of Hass Weir...

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he Cross Product The Cross Product Outline of Hass, Weir, Thomas – Section 9.4

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efinition Definition Let u and v be two non–zero vectors and let e e nit ector at rthogonal oth n be the unit vector that is orthogonal to both u v , determined by the right hand rule .(See Figure 9.26 in the textbook.) The cross product (a lsoca l ledthe vector product ), u v , is defined to be u v | u || v | sin n where is the angle between u v . ote ince ctor nd Note that since n is a unit vector and since 0 (and hence sin 0 ), then n | u v | | u v .
If one or both of u and v isthezerovector,thenwe define u v 0 . It follows from our definitions that u v 0 if and only if u v are parallel to each other (in which case 0 or ) or one or both of u v is thezero vector.

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ample Example 1) Compute i j and j i . et nd t ompute 2) Let u i j k and let v i j . Compute u v .
roperties of the Cross Product

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notes001 (7) - The Cross Product Outline of Hass Weir...

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