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- Find the curl of the vector field F(x,y,z)=x^2yi-2y^3zj-3zk. A. curl F = 2y3i + x2k B. curl F = -2y3i - x2k C. curl F = 2y3i - x2k D. curl F = -2y3i + kSketch the vector field F(x,y) → xi + 3yi - a. C. 'ீ, -10 10 -10 -5- L -10- 10- -10- 10 A R -10 10 10 10 b. d. -10 -10 10- IDA -10- וווו -10 10 10 d ரு VDFind the curl of the vector field F=(2xyz, -xy,-z^2)
- Find the work done by the vector field (5x + yx, x² + 3 ) or the boundary of the rectangle 0 < x< 3,0 < y < 6|in the counterclockwise direction. a particle moving along (The force is measured in newtons, length in meters, work in joules=(newton-meters).) W = joulesF = (x² - y)i + + (4z)j + (x²)k Find the curl (curl calculation) of the vector field?Where the vector field is (-y^2, x, z^2)
- Compute the curl of the vector field F = -6z i – 4yi- 6x k. curlDo the Lie derivative for the given vector field.The figure shows the vector field F (x,y) = {2xy,x2 } and three curves that start at (1,2) and end at (3,2). (a) Explain why∫c F. dr has the same value for all the three curves. (b) What is this common value?