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Sketching
F = ⟨1, y⟩
Sketch the vector field as shown below.
Step by step
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- using the vector function below, represent the vector fieldSketching vector fields Sketch the following vector field. F = ⟨2x, 3y⟩Flux Consider the vector fields and curve. a. Based on the picture, make a conjecture about whether the outwardflux of F across C is positive, negative, or zero.b. Compute the flux for the vector fields and curves. F and C given
- Sketching vector fields Sketch the following vector field. F = ⟨x, 0⟩Sketching vector fields Sketch the following vector field. F = ⟨e-x, 0⟩Curl of a rotation field Consider the following vector fields, where r = ⟨x, y, z⟩.a. Compute the curl of the field and verify that it has the same directionas the axis of rotation.b. Compute the magnitude of the curl of the field. F = ⟨1, -2, -3⟩ x r
- Sketch the vector fields. Use a table for it. F(x,y)=<x,y-x>Vector Calculus For scalar functions u and v, show that B = (Vu) × (Vv) is solenoidal and that A = - vVu) is a vector potential for B, i.e. B = V×APaddle wheel in a vector field Let F = ⟨z, 0, 0⟩ and let n be a unit vector aligned with the axis of a paddle wheel located on the x-axis (see figure).a. If the paddle wheel is oriented with n = ⟨1, 0, 0⟩ , in whatdirection (if any) does the wheel spin?b. If the paddle wheel is oriented with n = ⟨0, 1, 0⟩ , in whatdirection (if any) does the wheel spin?c. If the paddle wheel is oriented with n = ⟨0, 0, 1⟩ , in whatdirection (if any) does the wheel spin?