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Math · Advanced Math
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6. Consider the vector field w(z, y, z) := (-h(z)y, h (z)r, g(z)) where h : R → R and g : R → R are differentiable (i) Calculate ▽ × w(x, y,z). (ii) Let Ω be a bounded region in the horizontal plane z = a. (a) Write down a unit normal n to Ω. B) Explain what it means for a unit tangent t to 012 to be positively oriented with respect to n. (For positive you can read right-handed) (7) Show that the circulation of w around in depends only on the area of Ω and h (a).
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