DHS 15.2 - Option 22. Decisions Ryabushko AP

1. Calculate and circulation of the vector field (M) over the contour of a triangle obtained by intersection of the plane (p): Ax + By + Cz = D with the coordinate planes, with respect to the positive direction of the normal vector bypass n = (A, B, C) this plane in two ways: 1) using the definition of circulation; 2) using the Stokes formula.

1.22. a (M) = (x + y) i + 3yj + (y - z) k, (p): 2x - y - 2z = -2

2. Find the magnitude and direction of the greatest changes in the function u (M) = u (x, y, z) at the point M0 (x0, y0, z0)

2.22. u (M) = (x2 - y) z2, M0 (1, 3, 0)

3. Find the greatest density of the circulation of the vector field a (M) = (x, y, z) at the point M0 (x0, y0, z0)

3.22. a (M) = yzi - z2j + (x + y) zk, M0 (1, 3, 0)

4. Determine whether the vector field a (M) = (x, y, z) the potential

4.22. a (M) = (x + y) i + (z - y) j + 2 (x + z) k