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Solution -: To find a parametric representation bar(gamma)(u,v) for the given following surfacesand then finding to a hornd vector to the suiface(a) Plahe quad4x-2y+10 z=16Let x=4,y=vthen z=(16-44 t2v)/(10)Hence bar(gamma)(u,v)=(:u,v,(16-4u+2v)/(10):)Now for Normal vector to the given susface(affer parametrization) is given bybar(h)= bar(gamma)_(u xx bar(gamma))quad(1 bar(gamma)_(1):}" (ross product of "{:[ bar(gamma)_(u)=(:1,0,-(4)/(10):)],[ bar(gamma)_(v)=(:0,1,(2)/(10):)],[ bar(h)= bar(gamma)_(u)xx bar(gamma)_(v)=(:0-(i*(-(4)/(10)),0-(2)/(10),1-0:):}],[ bar(h)= bar(gamma)_(u xx)xx bar(gamma)_(v)=(:4//10,-(2)/(10),1:)]:}Hence (:(4)/(10),-(2)/(10),1) is nornal vector to the plaue(c) Parabolic cylinder z=3y^(2)=0.x+3y^(2) Let x=u,y=v{:[" then "z=3v^(2)],[" lie " b ... See the full answer