1. Find the line integral of the vector field along a path from (0,0) to (1,1).

1. Find the line integral of the vector field along a path from (0,0) to (1,1).

2. Calculate the line integral of the vector field along the following two paths joining the origin to the point P(1,1,1). (a) Along a straight line joining the origin to P, (ii) along a path parameterized by

3. From the result of Problem 2, can you conclude that the force is conservative? If so, determine a potential function for this vector field.

4. A potential function is given by , where *a, b* and *c *are constants. Find the force field.

5. A conservative force field is given by . Calculate the work done by the force in taking a particle from the origin to the point (1,1,2).

6. A force field is given by , where r is the distance of the point from the origin. Calculate the divergence at a point other than the origin.