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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