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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

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...
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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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