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It is by definition.

c = a X b
is called the cross product of a and b vectors.

Cross product is defined as the vector c whose direction is perpendicular to a and b both. Its direction is perpendicular to the plane of a and b.

Its magnitude is given by |a|  |b | Sin Ф,  where Ф is the angle between vectors.

Direction is given by curling the right hand fingers from direction of a to b, then the thumb points to the direction of c.

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