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DHS 15.2 - Option 27. Decisions Ryabushko AP
Uploaded: 09.11.2016
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)
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