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8. [5 marks] Bonus Question Let Q be a domain bounded by a closed smooth surface 2, and f(:r,y,z) be a scalar function dened on Q U 2. Assume that f has continuous second order partial derivatives and satises the Laplace equation on Q U E; that is, 32_f+ 82_f+ 621\" 3$2+ (By2 +3z2 =0 on Q U E. (i) Let n be the unit normal vector of E, pointing outward. Show that [/3111de (ii) Let ($0,191), 20) be an interior point in Q. Show that f(xo,yo,2o =/f (mSlilignb +|:|an) as where r = (:1: 2:0, 3; yo, 2 20) and (r, n) is the angle between the vectors r and n