Question: 5. Consider the vector field in R3 given by, F(x, y, z ) = xityj + (B+4)z k. Let Q be the three dimensional region

5. Consider the vector field in R3 given by, F(x, y,

5. Consider the vector field in R3 given by, F(x, y, z ) = xityj + (B+4)z k. Let Q be the three dimensional region contained within the unit cube as shown below: Z (0, 0, 1) . . " . . . . .. . . . . . . . ....... ............" (0, 1, 0) y (1, 0, 0) x (a) Calculate divF, the divergence of F. (b) Use Gauss' Divergence theorem, where 02 denotes the boundary of the unit cube (i.e. OQ consists of the six sides of the unit cube), to calculate 1/. F . n ds. [1 + 1 = 2 marks]

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