VECTOR ANALYSIS 



93 



4.20 



i. 



2. 



dAB = AdB+BdA. 

 dVAB = VAdB + VdAB 

 = VAdB - VBdA.. 



4.21 



i. 



Vasi +j +k 



dx dy dz 



,-7 A A- A dA x dAy dA z 



2. VA = dlV A = -T + -r + -TT 



4. FVA = curl A = rot A 

 i j k 



A A 



x d dz 



Id A, dA y \ .(dA, dA ,\ ISA _ dA x \ 

 -- ' -d^ + \dz dx)^\d X " dy) 



a 2 a- a ! 



= o. 



4.22 



1. curl grad < = curl V</> = 



a 2 c/) a 2 </> 



2. div grad </> = VV< = V 2 9 = ^r + ^Ti" 



3. div curl A = o. 



4. curl curl A = curl 2 A = V div A - V 2 A. 



5. V 2 A = iV 2 A* + ; 



6. 



