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: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

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: 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

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:

Q: Find r'(t), r(t), and r'(to) for the given value of to. r(t) = 3 cos(t)i + 3 sin(t)j, to r'(t) =…

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).…

A: