DHS 15.2 - Option 18. 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.

1.18. a (M) = (x + 2z) i + (y - 3z) j + zk, (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)

2.18. u (M) = (x + z) y2, M0 (2, 2, 2)

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

3.18. a (M) = xyi - xj + yzk, M0 (2, 2, 2)

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

4.18. a (M) = (x + y) i - 2xzj - 3 (y + z) k