explain the theory of conservative vector fields in details.
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explain the theory of conservative vector fields in details.
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- How do you determine whether a vector field in ℝ3 is conservative?Calculate the curl of the vector g = (x−y) ax+(y+x) ay, and visualize it. Explain what does "curl of vector field" mean, in your own words. When does it equal zero?Explain “ some combination gives the zero vector, other than the trivial combination with every x=0.”
- Using a graphic calculator, plot the vector field F(x, y) = j. Explain briefly with words why the plot x²+y? has this shape.A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the equation r1(t)=r2(t) may not produce all the points where the graphs of these functions intersect. Please Provide Unique Answer. Thank you!
