problems on derivative of vector functions : vector Calculus #vector #calculus #few #problems #& #solutions #on

***Few problems & Solutions on derivatives of a vector functions ***

Problem 1 :

              If r = a cost i + a sint j + at tanθ k then find (i) |(dr/dt)  x (d²r/dt²) |

                                                                                   (ii)  [ (dr/dt)    (d²r/dt²)   (d³r/dt³)  ]

Solution :

Problem 2 :

     If r= e^t (c cos2t+ d sin2t) where c and d are constant vectors, then show that d²r/dt² -2 dr/dt  +5r = 0.

Solution : 

Problem 3 :

           If r = t² i -t j + (2t+1) k, find the values of dr/dt ,d²r/dt²  , |dr/dt| and | d²r/dt² | at t=0.

Solution :

                   

Problem 4 :

            If A = 5t² i + t j -t³ k and B = sint i -cost j  then find a) d/dt (A.B ) 

                                                                                                b) d/dt ( AxB )  

                                                                                                c) d/dt ( A.A )

Solution :

    

Problem 5 :

       If r = x i + y j +z k  and x = 2 sin3t , y = 2 cos3t , z = 8t prove that | r’ | = 10 and | r ‘’ | = 18.

Solution :

                 

Problem 6 : 

                    If da/at = bxa , dc/dt = bxc , show that d/dt ( axc ) = bx(axc).

Solution :

               

Problem 7 :

    If a = sint i + cost j + t k , b = cost i – sint j -3 k and c= 2 i + 3 j – k then find [ ax ( b xc ) ]’ at t=0.

Solution :

   

Diaphantine Equation . 

line integrals .

Double integrals .

Historical introduction to integral calculus .

Historical introduction to Number Theory .

#integral #calculus #few #problems #& #solutions #on

#vector #calculus #vector calculus