DHS 15.2 - Option 26. 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.

1.26. a (M) = (y + 2z) i + (x + 2z) j + (x - 2y) k, (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)

2.26. u (M) = xz2 + y, M0 (2, 2, 1)

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

3.26. a (M) = (x - z) i + xyj + y2zk, M0 (2, 2, 1)

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

4.26. a (M) = x2zi + y2j - xz2k