92 MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



4.006 i, j, k are three unit vectors perpendicular to each other. If their direc- 

 tions coincide with the axes x, y, z of a rectangular system of coordinates: 



A = A x i + A y j + A 2 k. 



4.007 

 4.008 



4.009 

 4.010 



ii = i 2 = jj = j 2 = kk = k 2 = i, 

 ij = ji = jk = kj = ki = ik = o. 



Fij = - Fji = k, 

 Fjk = - Fkj = i, 

 Fki = - Fik = j. 



AB = BA = AB cos AB = A X B X + A y B y + A Z B 



FAB = - FBA = 



J 



B X By B Z 



= (A V B Z - A z B y )i+(A z B x - A x B,)j + (A X B V - A 



4.10 If A, B, C, are any three vectors: 



AFBC = BFCA = CFAB 



= Volume of parallelepipedon having A, B, C as edges 



A x A v A z 

 B x B y B z 



C x Cy C Z 



4.11 



1. FA(B + C) = FAB + FAC. 



2. F(A + B) (C + D) = FA(C + D) + FB(C + D). 



3. FAFBC = BSAC - CSAB. 



4. FAFBC + FBFCA + FCFAB = o. 



5. FAB-FCD = AC-BD - BC-AD. 



6. F(FAB-FCD) = C5(DFAB) - D5(CFAB) 



= CS(AFBD) - D5(AFBC) 

 = BS(AFCD) - A5(BFCD) 

 = B5(CFDA) - AS(CFDB). 



