The cross product of and is a vector denoted × . The magnitude of is given by
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where θ is the angle between and .
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The direction of is perpendicular to the plane formed by and , and obeys the right hand rule:
Position the middle and index fingers and thumb of your right hand at right angles with the index finger pointing straight. If the middle and index fingers approximate the directions of vectors and respectively, then the thumb will be in the direction of .
The components of cross product are expressed in terms of those for and as follows:
More compactly, the cross product can be written using a determinant:
where, , , and are unit vectors in the , , and directions respectively.
Note: (that is, the vector cross products are anticommutative).
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