Consider the 3-dimensional force field ⃗ F = (x^2 − ze^y)⃗i + (y^3 − xze^y)⃗j + (z^4 − xe^y)⃗k: (a) Show that ⃗ F is conservative. (b) If ⃗ F is conservative, find the corresponding potential function f (x, y)
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Consider the 3-dimensional force field ⃗ F = (x^2 − ze^y)⃗i + (y^3 − xze^y)⃗j + (z^4 − xe^y)⃗k:
(a) Show that ⃗ F is conservative.
(b) If ⃗ F is conservative, find the corresponding potential function f (x, y).
(c) If an object travels on a path ⃗r (t), (t_0 < t < t_f ), does the work done by
the force field depend on the path taken? Find the work done on the object moving
on the path ⃗r (t) by the force field ⃗ F , if ⃗r (t_0) = (3, 1, 2) and ⃗r (t_f ) = (6, 2, 5)
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