(10 points) Consider the inviscid Navier-Stokes equation for the velocity vector field v in Cartesian coordinates: av at + (v . Vv+-VP =F (1) p where P and p are spatially varying scalar functions. a) (3 points) For v = ux + vy + 0z, show that (v . V) v = ; V(v . v) - vx(Vxv). b) (3 points) Assuming V. v = 0 and V . w = 0, with v as in part a) and w = wz, show that V x ( v X w) = (w . V) v- (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 = Vxv) is aw at + ( v . V ) w - ( w . V ) v VP X VP = VXF 02 (2)