DHS 15.2 - Option 15. 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.

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

2.15. u (M) = 2x2yz, M0 (-3, 0, 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)

3.15. a (M) = xi - zyj + x2zk, M0 (-3, 0, 2)

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

4.15. a (M) = (2x - yz) i + (2x - xy) j + yzk