DHS 15.2 - Option 9. 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.

1.9. a (M) = (x + z) i + (x + 3y) j + yk, (p): x + 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)

2.9. u (M) = x2y + y2z, M0 (0, -2, 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)

3.9. a (M) = xyi - y2zj - xzk, M0 (0, -2, 1)

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

4.9. a (M) = (y + z) i + (x + z) j + (x + y) k