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Suppose that the vector field F(2, y, z) = (4y – 2z)î + (3y – 4z)j + (5æ + y)k and let the surface S be that part of the cone = 2 x + y? that lies inside the sphere x² + y? + z? = 8. The curve C of intersection of the upper half-cone and the sphere can be parametrized by the vector function А. 7(t) = 2 cos (t) î – 2 sin (t)ĵ + 4k, 0

Suppose that the vector field F(2, y, z) = (4y – 2z)î + (3y – 4z)j + (5æ + y)k and let the surface S be that part of the cone = 2 x + y? that lies inside the sphere x² + y? + z? = 8. The curve C of intersection of the upper half-cone and the sphere can be parametrized by the vector function А. 7(t) = 2 cos (t) î – 2 sin (t)ĵ + 4k, 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that the vector field F(x, y, z) = (4y – 2z)î + (3y – 4z)j + (5æ + y)k and let the surface S be that part of the cone + y? that lies inside the sphere x + y? + z2 = 8. The curve C of intersection of the upper half-cone and the sphere can be parametrized by the vector function A. 7(t) = 2 cos (t) i – 2 sin (t)j + 4k, 0<t< 2n. В. 7(t) = 2 sin (t)i + 2 cos (t)j + 4k, 0<t< 2r. %3D C. None of the listed alternatives. D. 7(t) = 2 cos (t) i + 2 sin (t)j ± 4k, 0<t< 2n.
Transcribed Image Text:Suppose that the vector field F(x, y, z) = (4y – 2z)î + (3y – 4z)j + (5æ + y)k and let the surface S be that part of the cone + y? that lies inside the sphere x + y? + z2 = 8. The curve C of intersection of the upper half-cone and the sphere can be parametrized by the vector function A. 7(t) = 2 cos (t) i – 2 sin (t)j + 4k, 0<t< 2n. В. 7(t) = 2 sin (t)i + 2 cos (t)j + 4k, 0<t< 2r. %3D C. None of the listed alternatives. D. 7(t) = 2 cos (t) i + 2 sin (t)j ± 4k, 0<t< 2n.
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