av +(v.)v+-VP=F at р (1) where P and p are spatially varying scalar functions. a) (3 points) For v = uân + vợ + Oź, show

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av +(v.)v+-VP=F at р (1) where P and p are spatially varying scalar functions. a) (3 points) For v = uân + vợ + Oź, show that (v.7)v= V(v.v) - vx(xv). b) (3 points) Assuming V.v = 0 and V.w = 0, with v as in part a) and w = wî, show that vx(vxw) = (w.)v-(v.)w. c) (4 points) Using these established tools, and assuming still that V.v = 0, but now v is a general vector field, take the curl of the Navier-Stokes equation to show that the equation for the vorticity (w = V xv) is aw +(v. Vw-(w.V)v XVP= VXF (2) at