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See also: Vector Definitions Vector Notation: The lower case letters ah, lz denote scalars. Uppercase bold AZ denote vectors. Lowercase bold i, j, k denote unit vectors. <a, b>denotes a vector with components a and b. <x_{1}, .., x_{n}>denotes vector with n components of which are x_{1}, x_{2}, x_{3}, ..,x_{n}. R denotes the magnitude of the vector R. <a, b> = magnitude of vector = (a^{ 2}+ b^{ 2}) <x_{1}, .., x_{n}> = (x_{1}^{2}+ .. + x_{n}^{2}) <a, b> + <c, d> = <a+c, b+d> <x_{1}, .., x_{n}> + <y_{1}, .., y_{n}>= < x_{1}+y_{1}, .., x_{n}+y_{n}> k <a, b> = <ka, kb> k <x_{1}, .., x_{n}> = <k x_{1}, .., k x_{2}> <a, b> <c, d> = ac + bd <x_{1}, .., x_{n}> <y_{1}, ..,y_{n}> = x_{1} y_{1} + .. + x_{n} y_{n}> 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 =  r_{1} r_{2} r_{3}  = / r_{2} r_{3} r_{3} r_{1} r_{1} r_{2} \  s_{1} s_{2} s_{3}  \ s_{2} s_{3} , s_{3} s_{1} , s_{1} s_{2} / 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 = RCOs = (R S) / S(scalar result) Projection of R in the direction of S = RCOs = (R S) S/ S^{ 2} (vector result)



