:I can't immediately spot this on either the Vector algebra relations or Vector calculus identities page, but you can easily prove it by expanding each of the terms according to
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A stronger mathematical definition is to use vector algebra, since a quantity with magnitude and direction, like the dipole moment of two point charges, can be expressed in vector form
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I ask because I'm not very familiar with vector algebra and this would help me finish a few proofs .-- talk ) 20 : 44, 19 August 2009 ( UTC)
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In a geometric algebra for which the square of any nonzero vector is positive, the inner product of two vectors can be identified with the dot product of standard vector algebra.
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Relevant is the distinction between axial and polar vectors in vector algebra, which is natural in geometric algebra as the distinction between vectors and bivectors ( elements of grade two ).
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The algebra was exploited by Peter Guthrie Tait and his school in Scotland, including James Clerk Maxwell, who composed his Maxwell's equations using the facility of vector algebra that quaternion algebra introduced.
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This is based on software that bypasses the inherent inaccuracy of the'Heading'function by recording data from the magnetometers and to the accelerometers, and then computing the orientation of the iPhone using vector algebra.
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The cross product of traditional vector algebra ( on \ mathbb { R } ^ 3 ) finds its place in geometric algebra \ mathcal { G } _ 3 as a scaled exterior product
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Many of these relationships only require the introduction of the exterior product to generalize, but since that may not be familiar to somebody with only a background in vector algebra and calculus, some examples are given.
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In fact, WP appears likely to have two new articles of mine, Vector algebra relations and Quadruple product, that will have been adopted as a result of my activities regarding the original AfD, and despite objections by Blackburne.
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