IV. VECTOR ANALYSIS 



4.000 A vector A has components along the three rectangular axes, x t y, z 



" *> " 0> " * 



A = length of vector. 



Direction cosines of A, % 4*, 4 s - 



.I .'1 A 



4.001 Addition of vectors. 



A + B - C. 



C is a vector with components. 



C,- 4,+ B 

 C 9 = A 9 + B 

 C,= A Z + B 



4402 = angle between A and B. 



C - V^ 2 + & +^2AB cos 0. 

 & _ AxBx-k-AyBi + A xBg 

 AB 



4.003 If a, b, C are any three non-coplanar vectors of unit length, any vector^ 



It, may be expressed: 



R = oa + ^b -3- re, 



where a, , care the lengths of the projections of R upon a, b, c respectively. 



4.004 Scalar product of two vectors: 



SAB = (AB) = AB 



are equivalent notations. ^ 



AB = AB cos 



4.006 Vector product of two vectors: 



FAB = A X B = [AB] = C. 



C is a vector whose length is ^ 



C= ABsinAB. 



The direction of C is perpendicular to both A and B such that a right-handed 

 rotation about C through the angje AB turns A into B. 



