An Introduction to Electrodynamics From the Standpoint of the Electron Theory

Cover An Introduction to Electrodynamics From the Standpoint of the Electron Theory
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Let a, b, and c be three vectors of the first order. Then the vector product a x b is a directed surface having for its area the parallelogram of which a and b are the sides, and so directed that bxa = axb.
Similarly, a X b x c is a directed volume having for its magni- tude that of the parallelepiped whose edges are a, b, and c. In the case of any cross product, interchange of two adjacent vectors changes the sign of the product.
Let k t, k 2, k 3, k 4 be unit vectors of the first order parall
...el respectively to the X, J, Z, L axes. Then * sk . X*.
is a unit vector of the second order in the YZ coordinate plane, and is a unit vector of the third order in the ZLX coordinate planoid. From their definition it is obvious that two adjacent subscripts of a unit vector of the second or third order may be interchanged provided the sign of the vector is changed.
The dot product of two unit vectors is defined as follows. If the vector of lower order has a subscript which the other lacks, the dot product vanishes.


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