1. UNIT-II VECTOR CALCULUS
IMPORTANT QUESTIONS:
PART-A
1. S.T
2. If is solenoidal find .
3. Find the directional derivatives of at (1,-2,-1) in the direction
4. Find the unit normal to the surface at (-1,1,1).
5. Find the angle between the surface (i) at (2,-1,2).
(ii) at (1,1,1).
6. Find a’ and b’ such that the surface a cut orthogonally at
(1,-1,2).
7. If then find the value of .
8. If ,then find
9. Find
10. Prove that Curl(curl ) = grad(div ) - .
11. P.T the vector = is solenoidal.
12. If = is solenoidal find ‘a’.
13. Determine f(r) so that the vector f(r) is solenoidal.
14. P.T = is irrotational.
15. Find the ‘a,’b,and’c so that is irrotational.
16. Prove is irrotational.and also find scalar potential.
17. If = .Evaluate form (0,0,0) to (1,1,1) along the curve
x=t, y=
18. Define GAUSS DIVERGENCE THEOREM?
19. Define STOKE’S THEOREM?
20. Define GREEN’S THEOREM?
21. Using Greens theorem to find area of the ellipse and area of the circle?

2. UNIT-II VECTOR CALCULUS
PRAT-B
1. Evaluate where =z
include in the first octant z = 0 and z = 5.
2. Evaluate where =
which is the first octant.
3. Evaluate where and S is the surface of the plane 2x+y+2z=6
in the first octant.
4. Verify Green’s theorem in the XY plane for where C is the
Boundary of the region given by x = 0,y = 0,x+y = 1.
5. Verify Green’s theorem in the XY plane for where C is the boundary of the
region given by y = x and y = .
6. Verify Green’s theorem in the XY plane for where C is the
boundary of the region given by x = ,y= .
7. Verify Green’s theorem in the XY plane for taken round the circle
8. Evaluate where C is the square formed by the line x = ±1, y = ±1.
9. Verify the G.D.T for over the cube bounded by x = 0,x = 1,y = 0, y = 1, z =0
,z = 1.
10. Verify the G.D.T for taken over the rectangular
parallelepiped 0 ≤ x ≤ a, 0 ≤ y ≤ b,0 ≤ z≤ c.(or) x = 0, x =a, y = 0,y = b, z =0 , z = c.
11. Verify G.D.T for the function over the cylinder region bounded by ,
z = 0 and z = 2.
12. Using the G.D.T of where and S is the sphere .
13. Verify Stokes theorem for the vector in the rectangular region bounded by
XY plane by the lines x = 0,x = a, y = 0, y = b.
14. Verify stokes theorem for where S is the surface bounded by the plane
x=0,x=1,y=0,y=1,z=0,z=1 above XY plane.
15. Verify stokes theorem for taken around the rectangle bounded by the lines
x = ±a, y = 0, y = b.
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