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How are vectors multiplied?

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Two different kinds of multiplication are defined for vectors in three dimensions. The scalar, or dot, product of two vectors, A and B, is a scalar, or quantity that has a magnitude but no direction, rather than a vector, and is equal to the product of the magnitudes of A and B and the cosine of the angle ? between them, or A ?? B ?=?&124; A &124; &124; B &124; cos ?. The vector, or cross, product of A and B is a vector, A ?×? B, whose magnitude is equal to &124; A &124; &124; B &124; sin ? and whose orientation is perpendicular to both A and B and pointing in the direction in which a right-hand screw would advance if turned from A to B through the angle ?.

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