Cross Product of 3D Vectors

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An interactive step by step calculator to calculate the cross product of 3D vectors is presented. As many examples as needed may be generated with their solutions with detailed explanations.

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.

Step by step solution

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