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Calc3.2.CrossProductProof (view source)
Revision as of 06:05, February 28, 2010
, 06:05, February 28, 2010→Putting it all together
===Putting it all together===
===Putting it all together===
Since the vectors <math>\vec{i},\vec{j},\vec{k}</math> are all perpendicular to each other, their cross products are very easy to compute:
<math>\vec{i}\times\vec{i}=\vec{0} \ \ \ \ \ \ \ \ \ \ \vec{i}\times\vec{j}=\vec{k} \ \ \ \ \ \ \ \vec{i}\times\vec{k}=-\vec{j} </math>
<math>\vec{j}\times\vec{i}=-\vec{k} \ \ \ \ \ \ \vec{j}\times\vec{j}=\vec{0} \ \ \ \ \ \ \ \vec{j}\times\vec{k}=\vec{i} </math>
<math>\vec{k}\times\vec{i}=\vec{j} \ \ \ \ \ \ \ \ \ \vec{k}\times\vec{j}=-\vec{i} \ \ \ \ \ \vec{k}\times\vec{k}=\vec{0} </math>
Using these formulas, and our identities, we can break take two vectors given by their components, and obtain the formula for the cross product. We leave this simple task as an exercise.
==Notes==
==Notes==
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