FORMULAE

Math Tables: Vectors (Math | Miscellaneous | Vectors) See also: Vector Definitions Vector Notation: The lower case letters a-h, l-z denote scalars. Uppercase bold A-Z denote vectors. Lowercase bold i, j, k denote unit vectors. <a, b>denotes a vector with components a and b. <x1, .., xn>denotes vector with n components of which are x1, x2, x3, ..,xn. |R| denotes the magnitude of the vector R. |<a, b>| = magnitude of vector = (a 2+ b 2) |<x1, .., xn>| = (x12+ .. + xn2) <a, b> + <c, d> = <a+c, b+d> <x1, .., xn> + <y1, .., yn>= < x1+y1, .., xn+yn> k <a, b> = <ka, kb> k <x1, .., xn> = <k x1, .., k x2> <a, b> <c, d> = ac + bd <x1, .., xn> <y1, ..,yn> = x1 y1 + .. + xn yn> R  S= |R| |S| cos ( = angle between them) R  S= S  R (a R)  (bS) = (ab) R  S R  (S + T)= R  S+ R  T R  R = |R| 2 |R x S| = |R| |S| sin ( = angle between both vectors). Direction of R x S is perpendicular to A & B and according to the right hand rule. | i j k | R x S = | r1 r2 r3 | = / |r2 r3| |r3 r1| |r1 r2| \ | s1 s2 s3 | \ |s2 s3| , |s3 s1| , |s1 s2| / S x R = - R x S (a R) x S = R x (a S) = a (Rx S) R x (S + T) = R x S + Rx T R x R = 0 If a, b, c = angles between the unit vectors i, j,k and R Then the direction cosines are set by:     COs a = (R  i) / |R|; COs b = (R  j) / |R|; COs c = (R  k) / |R| |R x S| = Area of parrallagram with sides Rand S. Component of R in the direction of S = |R|COs  = (R  S) / |S|(scalar result) Projection of R in the direction of S = |R|COs  = (R  S) S/ |S| 2 (vector result)