Image:Exterior calc cross product.png
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Summary
The cross product viewed in terms of the exterior product and Hodge dual. In red are the unit normal vector and unit "parallel" bivector. The cross product, as the dual of the bivector, has the same magnitude relative to the unit normal vector as the bivector has relative to the unit bivector -- thus the magnitude of the cross product is the area of parallelogram formed by the bivector.
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