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DHS 15.2 - Option 27. Decisions Ryabushko AP
Content: 27v-IDZ15.2.doc 108 kB
Product 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.
1.27. a (M) = (x + z) i + (z - x) j + (x + 2y + z) 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)
2.27. u (M) = x2y - z, 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)
3.27. a (M) = (x - z) i + xyzj + xk, M0 (-2, 2, 1)
4. Determine whether the vector field a (M) = (x, y, z) harmonic
4.27. a (M) = (x + y) i + (y + z) j + (x + z) k
Additional information
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)
For the convenience of viewing IDZ solutions on smartphones, an additional file in PDF format is sent
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