A(8, 3,8), B(9, 8,33), C(9, 5,12), D(9, 7,24) are four points in R3. Let E be the parallelepiped with three adjacent edges give by vectors AB, AC, AD (a) Find the volume of E. View E as a wire cage immersed in the ocean where there is a current with fluid velocity vector F(x,y,z) = (x+3z)i + (x+y)j + (y+3z)k . Find the flux of fluid out of the cage through all the six sides of E that comprise the bounding surface S of E. In other words, work out F. ds. (b) First choose the method you propose to use: O Apply the Fundamental Theorem for line integrals O Apply Stokes theorem, parametrize the curves and work out the line integrals O Apply Green's theorem and work out a double integral O Somehow parametrize the six surfaces C and calculate the surface integrals O Apply Fubini's Theorem O Apply the Divergence Theorem and work out a triple integral (c) Then give the answer: F. ds =

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

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A: Step 1: Step 2: Step 3: Step 4:

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A: Let's go through each of the questions:a. To find a nonzero vector perpendicular to both [−1,3,4]…