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Vector FormulasVector Formulas "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20060409 02:00:54
Re: Vector FormulasLet and be any two vectors.Properties: (i) Commutativity (ii) Associativity: (iii) Existence of a negative vector: For every vector , there is a negative such that If m and n are scalars, (iv) (v) (vi) (vii) (viii) Character is who you are when no one is looking. #3 20060409 02:20:16
Re: Vector FormulasScalar Product where is the angle between the two vectors. If and then and Character is who you are when no one is looking. #4 20060415 11:05:12
Re: Vector FormulasGanesh, you can use \cdot to produce: Last edited by Ricky (20060415 11:11:54) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #5 20060418 01:42:09
Re: Vector FormulasCross Product or Vector product Character is who you are when no one is looking. #6 20060420 00:26:58
Re: Vector FormulasScalar Triple Product then is also represented as Interchanging any two vectors in the scalar triple product changes the sign of the scalar triple product. If any of the two vectors are equal, then is the volume of the Parellopiped whose coterminus edges are formed by If are coplanar, Character is who you are when no one is looking. #7 20060420 01:45:50
Re: Vector FormulasVector Triple Product is defined as Vector triple product is not associative. Character is who you are when no one is looking. #8 20060421 00:49:33
Re: Vector FormulasScalar Product of four vectors Vector product of four vectors Vector product of four vectors is given by Character is who you are when no one is looking. #9 20060806 14:17:40
Re: Vector FormulasDerivative of a Vector Function Vector derivatives satisfy the following equations(note that Φ is a scalar function): Integral of a Vector Function If A(u) = dB/du, then we have the indefinite integral of A(u) and the definite integral of A(u) Last edited by Zhylliolom (20060806 16:10:32) #10 20060806 14:22:43
Re: Vector FormulasThe Operator Del/Nabla Gradient The gradient of Φ(x, y, z) is given by Divergence The divergence of A is given by Curl The curl of A is given by Last edited by Zhylliolom (20060806 15:17:27) #11 20060806 14:24:02
Re: Vector FormulasThe Laplacian The Biharmonic Operator The biharmonic operator ∇^{4} on Φ is given by ∇ Formulas For scalar functions Φ and Θ and vector functions A and B, the following equalities hold: Last edited by Zhylliolom (20060806 15:16:39) #12 20080312 08:00:51
Re: Vector FormulasThe equation of a line in vector form A vector equation of a straight line passing through the points C and D, with position vectors c and d respectively, is Where t is a scalar parameter. Last edited by Daniel123 (20080312 08:01:33) 