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The Proof of the Formula for the Vector Triple Product

Published online by Cambridge University Press:  03 November 2016

S. Chapman  and
E. A. Milne
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Extract

This note relates to the proof of the formula for the vector triple product (or continued vector product)

a ∧ (b ∧ c) = (a c) b − (a b)c, .....(1)

where the sign ∧ denotes vector multiplication and a dot denotes scalar multiplication.

Type
Research Article
Information
The Mathematical Gazette , Volume 23 , Issue 253 , February 1939 , pp. 35 - 38
Copyright
Copyright © Mathematical Association 1939 

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References

page no 36 note * Other proofs with a similar object have been given by Neville (Math. Gazette, XVII, 320, 1933) and Lowry (ibid., XVIII, 199, 1934). Our attention was drawn to these earlier proofs after this note was written, by the Editor.

page no 37 note * It can be shown that all orthogonal triads can be superposed on one or the other of two triads which cannot be so superposed; one of these is arbitrarily denoted as positive, the other as negative. Any triad can be deformed, by displacement of its rays through angles less than ½π into an orthogonal triad, and is positive or negative according to the sign of the resulting orthogonal triad. The vector product a ∧ b is then defined as such that a, b and a ∧ b form a positive triad. A positive triad may be “right-handed” or “left-handed”