Let F be the radial vector field F = x i + y j + z k. Show that if x(t), a t b, is any
Chapter 6, Problem 38(choose chapter or problem)
Let F be the radial vector field F = x i + y j + z k. Show that if x(t), a t b, is any path that lies on the sphere x 2 + y2 + z2 = c2, then x F ds = 0. (Hint: If x(t) = (x(t), y(t),z(t)) lies on the sphere, then [x(t)]2 + [y(t)]2 + [z(t)]2 = c2. Differentiate this last equation with respect to t.)
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