a. Show that the outward flux of the position vector field F = xi + yj +

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a. Show that the outward flux of the position vector field F = xi + yj + zk through a smooth closed surface S is three times the volume of the region enclosed by the surface.

b. Let n be the outward unit normal vector field on S. Show that it is not possible for F to be orthogonal to n at every point of S.

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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