The surface S₁ and vector field F are given, in Cartesian coordinates, by S₁ = {(x, y, z) : x² + y² + z² = 25, z ≥ 3} and F = (−y³, x³, z³), respectively. = A fluid flows through surface S₁ with velocity field u V x F, where F is given above. Show that u evaluates to (0, 0, 75 sin² 0) on the surface S₁, where is the polar angle for spherical polar coordinates. Hence, explicitly evaluate the surface integral == ]]s in order to calculate the volume flux Q of the fluid through the surface, in the direction away from the origin. Q u.dS,

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