Let T = ai + bj be a fixed unit vector, and letF = F(x, y)T be a vector field everywhere
Chapter 20, Problem 32(choose chapter or problem)
Let T = ai + bj be a fixed unit vector, and letF = F(x, y)T be a vector field everywhere parallel toT , but of varying magnitude F. Show that curl F equals k times the directional derivative of F in the direction ofF k . Do this in two ways:(a) Graphically, using line integrals(b) Algebraically(Note: The direction of F k is obtained by rotatingF through 90 clockwise as viewed from above the xyplane.)
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