5. Discuss real world quantities that the circulation of a vector field around a closed loop could measure? Now let F (1, 1). Sketch the vector field F at various points on the edges of the square. Based on your sketch, what value would you expect for the circulation of F around the perimeter of the square. Use Stokes' theorem to find the circulation of F for any closed loop C in space. yzi + zxj + yk. Draw a unit square in the xy plane with one corner at the origin and another at

. Consider the force vector F = x²a, -xza, -y²a. Calculate the work done in moving an object from point a to b along the path shown in Figure P1.36. C (1,0,0) X Z (0,0,1) a I (1,1,1) (0,1,0) y Figure P1.36 Contour of integra- tion of F.

Question 2. 1. Find the tangent plane equation and the normal unit vector of the sur- face z = x² + y² at the point (1,-1,2).

Q3