# DHS 15.2 - Option 29. Decisions Ryabushko AP

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# Description

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.

1.29. a (M) = (3x - 1) i + (y - x + z) j + 4zk, (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)

2.29. u (M) = y (x + z), M0 (0, 2, -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)

3.29. a (M) = (x - y) i - xj + xzk, M0 (0, 2, -2)

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

4.29. a (M) = yzi + xzj + xyk

Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)

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