Suppose F(x, y) = (2x – 2y, 6xy) and C is the line segment starting at (3, 0) and ending at (5, —4). (a) Find a vector parametric equation (t) for the line segment C. =(t) = (b) Find the circulation of along C. (Remember that the circulation of (P, Q) around the curve C is f Pdx + Qdy.) Circulation = (c) Find the outward flux of across C. (Remember that the outward flux of (P,Q) across the curve C is fo-Qdc + Pdy.) Flux =

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: The smooth vector-valued function P(t) satisfies P(2)= (-4, 8,-7), P′(2)= (0,-5,2), and P'(2)= (3,…

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Q: Let C = (-2, -1) be the center of dilation. Let X = (1, 1), Y = (3, 0) and Z = (2,5). Our dilation…

A: Center of dilation=-2, -1X=1, 1, Y=3, 0, Z=2, 5Dilation factor, k=3

Q: F(t) = (Cos(Tt), - 1), G(1) = (1, 1, – 1), G'(1) = (2, 3, 2) , Ĝ"(1) = (0, 1, 0) . (F.G) 1) (Gxở)…

A: Given :- F →t =  cos πt , e2t-1 , t2 - 1  , G →1 =  1 , 1 , -1G' →1 =  2, 3, 2G'' →1 =  0 , 1 , 0…

Q: he vector v = , is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

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Q: Give a vector parametric equation for the line that passes through the point (3, 5, –5), parallel to…

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Q: Sketch the curve which has the vector equation r(t) = cos ti + tj.

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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: tangent plane

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Q: Find T(t) ,N(t),B(t), and K(t) for the vector position r(t) = (e2t cos t) i + (e2t sin t)j + 2k when…

A: Given rt=e2tcosti+e2tsintj+2k

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A: The position vector is rt=2e-t, 6et and point 2, 6. We have to find the velocity vector vt, speed…

Q: Find the vector and parametric equations for the line through the point P(-2, 1, -5) and the point…

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Q: Assume that an object is moving along a parametric curve and the three vector function T (t), N(t) ,…

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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: iven belo

A: The value of derivative of vector R→t, R'→t=2e2t-4,6t2,1t-1  Integrating the derivative vector with…

Q: Find the vector and parametric equations for the line through the point P= (3,0, –1) and the point Q…

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: Consider the R − R 2 function r defined by r (t) = ￾ t, t2
; t ∈ [−3, 3] . (a) Determine the…

A: This is a problem of vector calculus.