or cross product, n. (Vector analysis) the product of two real vectors in three dimensions that is itself a vector, of which the magnitude is the product of the magnitudes of the given vectors and the sine of the angle between their directions, and of which the direction is perpendicular to the plane of the given vectors, forming a right-handed system. It is denoted v × w, or v ∧ w, and is equal to the determinant that is, so that |v × w | is the area of a parallelogram with sides v and w. The vector product is special to three dimensions but can be identified with the exterior product. Compare scalar product, vector triple product.