Suppose F(x, y) = (2y, - sin(y)) and C is the circle of radius 6 centered at the origin oriented %3D counterclockwise. (a) Find a vector parametric equation 7(t) for the circle C that starts at the point (6, 0) and travels around the circle once counterclockwise for 0 <1< 27. F() = (b) Using your parametrization in part (a), set up an integral for calculating the circulation of F around C. F. dr = FG0) F) dt = dt with limits of integration a = and b = (c) Find the circulation of F around C. Circulation =

Q: 5. (a) (b) The surfaces (x - 2)² + z² = 9 and y = z² intersect along the curve C. Find a vector…

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Q: how was it determined that the equation of the yz plane is x = 0?

A: The objective is to explain yz-plane equals .

Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: Write the parametric equation of the bilinear surface corresponding to four points P(0 0)= 0.25 0…

A: Given coordinates are, P0,0=0.25,0P1,0=0.75,0P0,1=0.75,0.9P1,1=0.25,0.8 So, the parametric equation…

Q: a) By first sketching its projection onto the yz-plane, sketch the curve r(t) = (t, cos(t), 2…

A: For (a), We will plot the sketch of r(t)=t, cos(t), 2 sin(t),  0≤t≤4π onto the yz-plane (that means…

Q: 32, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

A: The solution is given by

Q: Q2/ Find the Parametric aned standand equatior of the line Hhat passer through Points (-2,1,0)…

A: The equation of line passing through given two points is given as follows:

Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: Sketch the parametric curve of r(t) =.Then, find and draw the tangent vector r'(0)

A: 2cos t, 2sin t,3To Find:a. Sketch the parametric curve.b. Find and draw the tangent vector r'(0).

Q: equations

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Q: Solution r(t) = 6 cos(t) i + 6 sin(t)j + 3tk. The parametric equations for this curve are x= y = 6…

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Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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Q: tangent plane at the point (-2,1 – 3)

A: Equation of the tangent plane = dfdxx-x0+dfdyy-y0+dfdzz-z0 Let f=x24+y2+z29-3 (given)

Q: Suppose F(x, y) = x² + y²j and C is the line segment segment from point P = (-3,-4) to Q = (-3, 1).…

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Q: Find the points (x, y) on the curve with the parametric equations (x3Dt3- 4t at ly=t +2 which the…

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