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I. Use the Divergence Theorem: (² F. ds = Ifv. Fav SSS E = to calculate the flux of the field F intersection of plane the with the coordinate axis planes. (-y, x, z) through the tetrahedron formed by the

I. Use the Divergence Theorem: (² F. ds = Ifv. Fav SSS E = to calculate the flux of the field F intersection of plane the with the coordinate axis planes. (-y, x, z) through the tetrahedron formed by the

Elementary Geometry for College Students
Elementary Geometry for College Students
6th Edition
ISBN:9781285195698
Author:Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:Daniel C. Alexander, Geralyn M. Koeberlein
Chapter10: Analytic Geometry
Section10.CT: Test
Problem 3CT
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6. Complete the following for plane A. Write an equation of plane B. Sketch the plane in the first octant of a right hand system. C. Find the point on the plane that is closest to the origin. D. Calculate the surface area of the triangular region formed by the intersection of the plane with the coordinate axis planes. with axis intercepts P(3, 0, 0), Q(0, 2, 0), & R(0, 0, 6). as ax + by + cz = d where a, b, c, and d are integers. E. Calculate the volume of the tetrahedron formed by the intersection of the plane with the coordinate axis planes. F. Use Green's Theorem to calculate the circulation in the presence of F(-y², x) around the triangular region in the xy-plane region formed the intersection of the plane with the coordinate axis planes. That is, set D is the triangle with vertices at the origin, P(3, 0), and Q(0, 2). G. Use Green's Theorem to calculate the flux of F = (-y2, x) with upward pointing normal vector through the triangular region in the xy-plane region formed the intersection of the plane with the coordinate axis planes. That is, set D is the triangle with vertices at the origin, P(3, 0), and Q(0, 2). H. Calculate the circulation in the presence of the field = (-y, x, z) around the curve C: the triangular region formed by the intersection of the plane with the coordinate axis planes using Stoke's Theorem: S I. Use the Divergence Theorem: 7x F. ds = D VXF ñ dA. ff # · ds = fff S E 7. F dv to calculate the flux of the field = (-y, x, z) through the tetrahedron formed by the intersection of plane & the with the coordinate axis planes.
Transcribed Image Text:6. Complete the following for plane A. Write an equation of plane B. Sketch the plane in the first octant of a right hand system. C. Find the point on the plane that is closest to the origin. D. Calculate the surface area of the triangular region formed by the intersection of the plane with the coordinate axis planes. with axis intercepts P(3, 0, 0), Q(0, 2, 0), & R(0, 0, 6). as ax + by + cz = d where a, b, c, and d are integers. E. Calculate the volume of the tetrahedron formed by the intersection of the plane with the coordinate axis planes. F. Use Green's Theorem to calculate the circulation in the presence of F(-y², x) around the triangular region in the xy-plane region formed the intersection of the plane with the coordinate axis planes. That is, set D is the triangle with vertices at the origin, P(3, 0), and Q(0, 2). G. Use Green's Theorem to calculate the flux of F = (-y2, x) with upward pointing normal vector through the triangular region in the xy-plane region formed the intersection of the plane with the coordinate axis planes. That is, set D is the triangle with vertices at the origin, P(3, 0), and Q(0, 2). H. Calculate the circulation in the presence of the field = (-y, x, z) around the curve C: the triangular region formed by the intersection of the plane with the coordinate axis planes using Stoke's Theorem: S I. Use the Divergence Theorem: 7x F. ds = D VXF ñ dA. ff # · ds = fff S E 7. F dv to calculate the flux of the field = (-y, x, z) through the tetrahedron formed by the intersection of plane & the with the coordinate axis planes.
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