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    Vector Product

    Illustration

    Illustration

    Alternate names

    vector cross product | vector product

    Basic definition

    The cross product is a product of two vectors that results in a vector perpendicular to both.

    Detailed definition

    For vectors u = (u_x, u_y, u_z) and v = (v_x, v_y, v_z) in R^3, the cross product in is defined by uxv | = | x^^(u_y v_z - u_z v_y) - y^^(u_x v_z - u_z v_x) + z^^(u_x v_y - u_y v_x) | = | x^^(u_y v_z - u_z v_y) + y^^(u_z v_x - u_x v_z) + z^^(u_x v_y - u_y v_x), where (x^^, y^^, z^^) is a right-handed, i.e., positively oriented, orthonormal basis.

    Related terms

    Cartesian product | determinant | dot product | permutation symbol | right-hand rule | scalar triple product | vector | vector direct product | vector multiplication

    Related Wolfram Language symbol

    Cross

    Educational grade level

    high school level

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