3. If A = (2xy + z³)ŵ + (x² + 2y)ŷ + (3xz² + 5)2, then (a) Evaluate V x A (b) Based on the answer to (a) and the second derivative identity VX (Vf) = 0, it seems probable that A = Vf for some scalar function f. Show that this is indeed the case for f = x²y + xz³ + y² + 5z.
3. If A = (2xy + z³)ŵ + (x² + 2y)ŷ + (3xz² + 5)2, then (a) Evaluate V x A (b) Based on the answer to (a) and the second derivative identity VX (Vf) = 0, it seems probable that A = Vf for some scalar function f. Show that this is indeed the case for f = x²y + xz³ + y² + 5z.
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Transcribed Image Text:3. If A = (2xy + z³)ŵ + (x² + 2y)ŷ + (3xz² + 5)2, then
(a) Evaluate V x A
(b) Based on the answer to (a) and the second derivative identity VX (Vf) = 0, it seems probable that A =
Vf for some scalar function f. Show that this is indeed the case for f = x²y + xz³ + y² + 5z.
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