Q2. (a) Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k. (i) Determine whether if F is conservative or not. (ii) Find the potential function of F and evaluate it at the point A(1,3, 2).
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Q: Q2. (a) Given a vector field, F = 2xyi + (x² + 3y²z)j+ (y³ + 2z)k. Find the potential function of F…
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- F = (x² - y)i + + (4z)j + (x²)k Find the curl (curl calculation) of the vector field?1) Find the domain of the vector-valued function r(t) = (3t+1,6,ln(9-t)).A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v = (x-y, z + y + 3, z²) and the net is decribed by the equation y = √1-x²-2², y ≥ 0, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)
- F(x, y) = x²yi + 3y³x²j Find the integral curves for the vector field а. —6у + 1 = C 6xy2 ob. -6ху — 1 C 6xy2 c. -6ху + 1 = C 6x²y2 O d. -ху + 6 C x?y2·SoF F.Tds for the vector field F = x²i+yj along the curve x = y2 from (1,1) to (4,-2). Evaluate SoF F.Tds= (Type an integer or a simplified fraction.)A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)