Cross Product of 3D Vectors

The cross (or vector) product of two vectors \( \vec{u} = (u_x , u_y ,u_z) \) and \( \vec{v} = (v_x , v_y , v_z) \) is a vector quantity defined by:

definition of cross product

The cross product \( \vec{u} \times \vec{v} \) is perpendicular to both \( \vec{v} \) and \( \vec{u} \)

The right hand rule, to find the direction of the cross product, is as follows: point the index in the direction of \( \vec {u} \), the middle finger in the direction of \( \vec{v} \) and the direction of the cross product \( \vec {u} \times \vec {v} \) is in the same direction as that of the thumb.

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