1. If vector F =(y2-z2+3yz-2x)i+(3xz+2xy)j+(3xy-2xz+2z)k, then prove that vector F is both irrotational and solenoidal.
2. Evaluate the line integrals ∫c[(x2+xy)dx+(x2+y2)dy], where C is the square formed by the line y± 1 and x=±1
3. Verify Gauss's divergence theorem for vector F =(x2-yz)i+(y2-zx)j+(z2-xy)k, taken over the rectangular parallelopiped 0 ≤ x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ c.
