DHS 15.2 - Option 14. 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.

1.14. a (M) = (x + y) i + (y + z) j + 2 (x + z) k, (p): 3x - 2y + 2z = 6

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)

2.14. u (M) = xyz2, M0 (4, 0, 1)

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

3.14. a (M) = xyi - (y + z) j + xzk, M0 (4, 0, 1)

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

4.14. a (M) = 6xyi + (3x2 - 2y) j + zk