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DHS 15.2 - Option 12. Decisions Ryabushko AP
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Uploaded: 17.01.2024
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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.
1.12. a (M) = (2x - z) i + (y - x) j + (x + 2z) k, (p): x - y + 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)
2.12. u (M) = x2yz, M0 (1, -1, 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)
3.12. a (M) = xyi - xy2j - xy2j + z2k, M0 (1, -1, 1)
4. Determine whether the vector field a (M) = (x, y, z) the potential
4.12. a (M) = (yz - 2x) i + (xz + zy) j + xyk
Additional information
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
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