DHS 15.2 - Option 17. 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.

1.17. a (M) = 4xi + (x - y - z) j + (3y + 2z) k, (p): 2x + y + z = 4

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)

2.17. u (M) = (x + y) z2, M0 (0, -1, 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)

3.17. a (M) = xzi - yj + yzk, M0 (0, -1, 4)

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

4.17. a (M) = (y - z) i + (x + z) j + (x2 - y2) k