School of Mathematics and Statistics, The University of Sydney
 11. The vector product
Main menu Section menu   Previous section Next section The vector product in terms of magnitudes, angles and the “right-hand rule” Derivation of the formula
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The vector product in terms of components

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If u = u1i + u2j + u3k and u = v1i + v2j + v3k are two vectors then their vector product is

u × v = (u2v3 - u3v2)i + (u3v1- u1v3)j + (u1v2 - u2v1)k.

If you are familiar with determinants of a 3 × 3 matrix, there is an easy way to remember the above formula. Formally,

|| i j k || | | | | | | || || ||u2 u3|| ||u1 u3|| ||u1 u2|| u × v = |u1 u2 u3| = |v2 v3|i- |v1 v3|j + |v1 v2| k. |v1 v2 v3|

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Main menu Section menu   Previous section Next section The vector product in terms of magnitudes, angles and the “right-hand rule” Derivation of the formula