Question I Engineering Mathematics 2 a) A fluid material moves in 3 dimensional space with the following vector flow equ

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Question I Engineering Mathematics 2 A A Fluid Material Moves In 3 Dimensional Space With The Following Vector Flow Equ 1 (33.82 KiB) Viewed 11 times

Question I Engineering Mathematics 2 a) A fluid material moves in 3 dimensional space with the following vector flow equation: = 10(sin(x)) + zyj + yzk Determine whether the vector flow converges or diverges at point (0.5, -10, 94). Explain your answer. b) The temperature, T = T(x, y, z), of a certain object is given by T(x, y, z)= 93xy In(z) i. Calculate the rate of change of the temperature (directional derivative) at coordinate (2, 3,94) in the direction of a = i + 2) + 3k. Show your derivations. i. Determine whether it is possible to have a directional derivative of -55 at coordinate (2, 3, 94). Explain your answer. (Hint: Calculate the lowest directional derivative value). Question 2 Assume an object is moving from A(- k, k², 0) to B(2k, 4k², 0) along the path F=< t, t²,0>, where k = 1. The object is subjected to force, F =< xsiny, y, yz). a) Find the work done for the object moving from A to B by using integral. b) Without integral calculation, estimate the total work done for the object moving from A to B and back to A following the same path