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It contrasts with the dot product which produces a scalar result. In many engineering and physics problems, it is handy to be able to construct a perpendicular vector from two existing vectors, and the cross product provides a means for doing so. The cross product is also useful as a measure of perpendicularness\–the magnitude of the cross product of two vectors is equal to the product of their magnitudes if they are perpendicular and scales down to zero when they are parallel. The cross product is also known as the vector product. In mathematics, the cross product is a binary operation on two vectors in a three-dimensional Euclidean space that results in another vector which is perpendicular to the plane containing the two input vectors. The algebra defined by the cross product is neither commutative nor associative. The cross product is only defined in three or seven dimensions. Like the dot product, it depends on the metric of Euclidean space. Unlike the dot product, it also depends on the choice of orientation or handedness. Certain features of the cross product can be generalized to other situations.