DHS 15.2 - Option 3. 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.

1.3. a (M) = (y + z) i + xj + (y - 2z) k, (p): 2x + 2y + 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)

2.3. u (M) = xy2z, M0 (-1, -2, 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)

3.3. a (M) = xy2i + yz2j - x2k, M0 (-1, -2, 0)

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

4.3. a (M) = (yz - 2x) i + (xz + 2y) j + xyk