DHS 15.2 - Option 20. 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.

1.20. a (M) = (y - z) i + (2x + y) j + zk, (p): 2x + y + z = 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)

2.20. u (M) = (x2 + z) y2, M0 (-4, 1, 0)

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

3.20. a (M) = (x - y) i + yzj - yk, M0 (-4, 1, 0)

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

4.20. a (M) = xy (3x - 4y) i + x2 (x - 4y) j + 3z2k