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: 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…

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A:

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A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: If the gradient of f is Vƒ = z j - yi – 2xzk and the poi f(x, y, z) = 0, find an equation for the…

A:

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

A:

Q: The curves ri(t) = (4t-t²,3t, ²-4) and r₂(t) = (4-t,t³ +8,5t) intersect at the point (3,9,5). If u…

A: Tangent vectors and vector perpendicular to them

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A: The vector parametric equation of the line that passes through the points: A=x1, y1, z1, B=x2, y2,…

Q: Let f(x, y) = 10-3r² +4. (a) Find the gradient Vƒ(2,-3) of f at the point P(2,−3). (b) Find the…

A:

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A: Given rt=e2tcosti+e2tsintj+2k

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A: The given vector valued function

Q: 1. Let ř(t) = (In |t – 1|, e', vi ) (a) Express the vector valued function in parametric form. (b)…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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: 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.