Vector Product

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Vector Product

A vector whose magnitude is equal to the product of the magnitudes of any two given vectors and the sine of the angle between their positive directions. Also called cross product, outer product. See scalar product. For two vectors A and B, the vector product is often written A X B (read A cross B), and defines a vector perpendicular to both A and B and so directed that a right-hand rotation about A X B through an angle of not more than 180 degrees carries A into B. The magnitude of A X B is equal to twice the area of the triangle of which A and B are coterminous sides. IF the vector product is zero, one of the vectors is zero or else the two are parallel. When A and B are written in terms of their components along the X-, Y-, and Z-axes of the rectangular Cartesian coordinates, i.e.,

A = a1i + a2j + a3k
B = b1i + b2j + b3k

then the vector product is the determinant

Missing Image:img src="SP7_v_files/vecprod.gif" alt="vector product"
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This article is based on NASA's Dictionary of Technical Terms for Aerospace Use