VC3.43

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Here the equation of the given surface is \phi (x,y,z)=x^{2}+y^{2}-z=0\,

Then we know that \nabla \phi \, is a vector normal to the above surface at (x,y,z).

Now,\nabla \phi =[i{\frac  {\partial }{\partial }}+j{\frac  {\partial }{\partial y}}+k{\frac  {\partial }{\partial z}}](x^{2}+y^{2}-z)=2xi+2yj-k=-2i-4j-k\, at (-1,-2,5).

Therefore,unit vector to the surface given,at(-1,-2,5)={\frac  {\nabla \phi }{|\nabla \phi |}}={\frac  {-(2i+4j+k)}{{\sqrt  {2^{2}+4^{2}+1^{2}}}}}=-{\frac  {2i+4j+k}{{\sqrt  {21}}}}\,

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