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 =

Q: Find the dot product of a = and b = .

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A: here we have to find the unit vector.

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A: Here, we need to find the binormal vector B. We are given that r(t)=&lt;x(t), y(t), z(t)&gt; where…

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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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Q: Find the unit vector in the direction of

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