6. a) Provethatdivl{ilnd)161
: -2i.d,whererl:xi+yj +zk, d:
*a:kandS:bri+bzj+b:k
b) Prove that curl ($ fr) : (grad S) *il + fi curtT'
7. a) IfF:(ara*y'uli+(3y- 4x) j,thenevaluatef
b)
a1i+arj
F dialongthetriangle
ABC where vertices are A(0,0) , B(2,0) , C(2,1).
verifu the stoke's theorem for the function F: x{rr*y;} integrated
around the square in the plane z: 0 whose sides are along the lines X : 0,
Y:0rX:&rY:a
8. Write short notes on (any Three):a) Simply connected domain
b) Change of Variables
c) Length of Curves
d) Stokes'Theorem
e) Divergence
and curl.of,a vector function
,