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.

1.1. a (M) = zi + (x + y) j + yk, (p): 2x + 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)

2.1. u (M) = xyz, M0 (0, 1, -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)

3.1. a (M) = x2i - xy2j + z2k, M0 (0, 1, -2)

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

4.1. a (M) = (α - β) xi + (γ - α) yj + (β - γ) zk

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