Scalar Product

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Scalar Product

</dt>
A scalar equal to the product of the magnitudes of any two vectors and the cosine of the angle θ between their positive directions. Also called dot product, direct product, inner product. See vector product. </dd>
For two vectors A and B, the scalar product is most commonly written A ^. B, read A dot B, and occasionally as (AB). If the vectors A and B have the components A_x, B_x, A_y, B_y, and A_z, B_z along rectangular Cartesian, x, y, and z axes, respectively, then

A ^. B = A_xB_x + A_yB_y + A_zB_z = |A||B|cosθ = AB cosθ

If a scalar product is zero, one of the vectors is zero or else the two are perpendicular. </dd>

References

This article is based on NASA's Dictionary of Technical Terms for Aerospace Use