The cross product equals to the area of the parallelogram defined by the two vectors (at least in R^3). So if working on vectors which units(adsbygoogle = window.adsbygoogle || []).push({});

v_1 = (1,2,3)m

v_2 = (3,4,5)m

it correctly returns the according area. However, if used to get a vector perpendicular to each of the vectors the resulting vectors has the unit m^2.

How does this fit together? Whats the term for the "dimension" of this vector anyway, since it's actual dimension is 3 (am I mistaken here?) as in the field of R^3.

Thanks for your help, PF

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# The logic behind the cross product with units

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