A vortex that rotates at constant angular velocity w about the z-axis has velocity vector field v = w(-yn + x). ) Sketch, on a separate sheet of paper, the vector field with w = 1 and the vector field with w = the distance from its center, r. 1. Then determine the speed ||v|| of the vortex as a fu peed = -) Compute div v and curl v. iv v = -wx+wy url = k(xwx+ywy) ) Compute the circulation of v counterclockwise about the circle of radius R in the ay-plane, centered at the origin. Tculation =

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A: To write the vector v in the form ai+bj, given its magnitude v and the angle α it makes with the…

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Q: Find the magnitude of the vector  , 3−6 .   Write your answer in simplified radical form.

A: Let the vector be u=3,-6. To determine the magnitude of the vector v=x,y, use the formula v=x2+y2.

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A: Equation of line in vector form is:r→=a→+λb→Where,a→=x1i→+y1j→+z1k→ b→=b1i→+b2j→+b3k→

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Q: 8. Find a vector that has the opposite direction as u = but has length 4.

A: