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Properties of the cross product

Like the dot product, the cross product has some nice properties. It's easy to see that tex2html_wrap_inline718 .

Also if two vectors are going in the same direction, the cross product is zero. If the vectors are perpendicular then tex2html_wrap_inline720 so that the magnitudes just multiply. Let's work out some of the cross products between unit vectors:


So now we should be able to work out the cross product in cartesian coordinates by multiplying out all of the components. It's a lot of work and the answer is


The component formula is usually the simplest way to work out problems involving cross products.

Joshua Deutsch
Sun Feb 23 15:54:50 PST 1997