2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: Find the curl, the divergence and the potential (if it exists) of F = (2x + y², 2ry + 3y²z*, 4y°z³)

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Q: 3. Let F = (x - y, xy) and C be arc of the circle x? + y? = 4 traversed counter-clockwise from (2,0)…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given: The velocity vector field v=x-y, z+y+6, z2. The net is described by the equation y=1-x2-z2…

Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

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Q: 2) Sketch the curve with the vector equation r(t) = costi- costj+ sin tk. Show the direction of…

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Q: Find the curl of the vector field F = (3y cos(x), 5x sin(y))

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Q: Find the curl of the vector field F (6x sin(y), 2y cos(x)). curl F =

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Q: Find the curl of the vector field F = (5y cos(x), 4x sin(y)) curl F -

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Q: Find the curl of the vector field F curl F= (5y cos(x), 2x sin(y)).

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Q: Plot the vector field F = (y,sinx) using the viewing window (-2pi,2pi)x(-2pi,2pi

A: Given:       F = ( y , sin(x) )      viewing window :  (-2pi  ,  2pi)

Q: Let r(t)=(10 cos(t), 1, 10 sin(t)). Find the unit tangent vector u drawn to point P=(6,1,8). Sketch…

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Q: The vector function r(t) = (1+2 cost) i+3j+(5 – 2 sin t) k | traces out a circle in 3-space as t…

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