problems on derivative of vector functions : vector Calculus #vector #calculus #few #problems #& #solutions #on
***Few problems & Solutions on derivatives of a vector functions ***
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 :
If r= et (c cos2t+ d
sin2t) where c and d are constant vectors, then show that d2r/dt2
-2 dr/dt +5r = 0.
Solution :
Problem :
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 :
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 :
If r = x i + y j +z k
and x = 2 sin3t , y = 2 cos3t , z = 8t prove that | r’ | = 10 and | r ‘’
| = 18.
Problem :
If da/at = bxa , dc/dt = bxc , show that d/dt ( axc ) =
bx(axc).
Problem :
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.
#integral #calculus #few #problems #& #solutions #on
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