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- F = (x² - y)i + + (4z)j + (x²)k Find the curl (curl calculation) of the vector field?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.)Let R be a differentiable vector-valued function such that R'(t) = (3t2,2tvt? + 1, 2t + 3) and R(1) = (4, *2, 3). Find R(0).
- Find the upward flux of F = (14e*, -7e, -6) through the first-octant part of the triangle x+2y+3z = 6. Answer: ESketch the vector field represented by F (x, y) = (-x,y)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