Schwere, Elektricität und Magnetismus:380

Bernhard Riemann: Schwere, Elektricität und Magnetismus
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VECTOR ANALYSIS.


two components, and , respectively parallel and perpendicular to . Then





Hence,


 27. General relation of the vector products of three factors.—In the triple product we may set



unless and have the same direction. Then



But and


Therefore


which is evidently true, when and have the same directions. It may also be written



 28. This principle may be used in the transformation of more complex products. It will be observed that its application will always simultaneously eliminate, or introduce, two signs of skew multiplication.

 The student will easily prove the following identical equations, which, although of considerable importance, are here given principally as exercises in the application of the preceding formulae.


 29.

 30.

 31.

 32.

 33.[1]

 34.



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