The following identities may be useful for H6.1! r; are the components of r: 1 = x, 12 =y, 13 =Z. r is the magnitude of r: r= Irl = Vx2+ y2 + z. Gradient operator: Vied; = in Cartesians Product rule: n'An+ AAn= (An)'s Quotient rule: Vi (4 ) = VVU-UVV v2 Chain rule: - = ((1)4)n's du ov " V. V. ar av ar; av Vir= 1. Proof: Vir = or= - ar; ar; riri 2 areF ar ("jr; ) = 2, 26,jr; = 2. Viri =dij. Proof: Virjar; r;= 1 only if i = j; otherwise it is zero. H6.1: Vector calculus practice Show that (a) Vi-= ( b ) Vivi- (c) ViviVK= =