Vector quadruple product

Vector quadruple product

The vector quadruple product of four vectors A, B, C and D in three dimensions is defined as:

: (mathbf{A} imes mathbf{B}) cdot (mathbf{C} imes mathbf{D}) = (mathbf{A} cdot mathbf{C})(mathbf{B} cdot mathbf{D}) - (mathbf{A} cdot mathbf{D})(mathbf{B} cdot mathbf{C})

where the "×" and "·" symbols denote respectively the cross product and dot product.

A quadruple product which is also a vector can be defined, which satisfies the following identities:

: (mathbf{A} imes mathbf{B}) imes (mathbf{C} imes mathbf{D}) = (mathbf{A} imes mathbf{C})(mathbf{B} cdot mathbf{D})+(mathbf{B} imes mathbf{D})(mathbf{A} cdot mathbf{C}) - (mathbf{A} imes mathbf{D})(mathbf{B} cdot mathbf{C})-(mathbf{B} imes mathbf{C})(mathbf{A} cdot mathbf{D})

and : (mathbf{A} imes mathbf{B}) imes (mathbf{C} imes mathbf{D}) = [mathbf{A},mathbf{B}, mathbf{D}] mathbf{C}- [mathbf{A},mathbf{B}, mathbf{C}] mathbf{D}= [mathbf{A},mathbf{C}, mathbf{D}] mathbf{B}- [mathbf{B}, mathbf{C},mathbf{D}] mathbf{A}

where [mathbf{A},mathbf{B}, mathbf{C}] is the scalar triple product.

ee also

*Cross product
*Triple product

References

*cite book|last = Lass|first = Harry|title = Vector and Tensor Analysis|publisher = McGraw-Hill Book Company, Inc.|date = 1950|pages = p. 25

External links

*Mathworld|urlname = VectorQuadrupleProduct|title = Vector Quadruple Product


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Vector Analysis (Gibbs/Wilson) — Vector Analysis is a book on vector calculus first published in 1901 by Edwin Bidwell Wilson. Its subtitle is A Text book for the use of students of mathematics and physics, founded upon the lectures of J. Willard Gibbs Ph.D. LL.D. This textbook… …   Wikipedia

  • vector analysis — the branch of calculus that deals with vectors and processes involving vectors. * * * ▪ mathematics Introduction       a branch of mathematics that deals with quantities that have both magnitude and direction. Some physical and geometric… …   Universalium

  • List of mathematics articles (V) — NOTOC Vac Vacuous truth Vague topology Valence of average numbers Valentin Vornicu Validity (statistics) Valuation (algebra) Valuation (logic) Valuation (mathematics) Valuation (measure theory) Valuation of options Valuation ring Valuative… …   Wikipedia

  • Quaternion — Quaternions, in mathematics, are a non commutative extension of complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three dimensional space. They find uses in both… …   Wikipedia

  • Mathieu group — Group theory Group theory …   Wikipedia

  • List of mathematics articles (P) — NOTOC P P = NP problem P adic analysis P adic number P adic order P compact group P group P² irreducible P Laplacian P matrix P rep P value P vector P y method Pacific Journal of Mathematics Package merge algorithm Packed storage matrix Packing… …   Wikipedia

  • Abkürzungen/Computer — Dies ist eine Liste technischer Abkürzungen, die im IT Bereich verwendet werden. A [nach oben] AA Antialiasing AAA authentication, authorization and accounting, siehe Triple A System AAC Advanced Audio Coding AACS …   Deutsch Wikipedia

  • Liste der Abkürzungen (Computer) — Dies ist eine Liste technischer Abkürzungen, die im IT Bereich verwendet werden. A [nach oben] AA Antialiasing AAA authentication, authorization and accounting, siehe Triple A System AAC Advanced Audio Coding AACS …   Deutsch Wikipedia

  • Pythagorean triple — A Pythagorean triple consists of three positive integers a , b , and c , such that a 2 + b 2 = c 2. Such a triple is commonly written ( a , b , c ), and a well known example is (3, 4, 5). If ( a , b , c ) is a Pythagorean triple, then so is ( ka …   Wikipedia

  • Total order — In set theory, a total order, linear order, simple order, or (non strict) ordering is a binary relation (here denoted by infix ≤) on some set X. The relation is transitive, antisymmetric, and total. A set paired with a total order is called a… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”