DHS 15.2 - Option 16. 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.

1.16. a (M) = (2z - x) i + (x + 2y) j + 3zk, (p): x + 4y + 2z = 8

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)

2.16. u (M) = x2yz, M0 (1, 0, 4)

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

3.16. a (M) = (x + y2) i + yzj - x2k, M0 (1, 0, 4)

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

4.16. a (M) = (y - z) i + 3xyzj + (z - x) k