Calculus 3 Quiz
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VECTOR FIELDS & LINE/SURFACE INTEGRALS
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Consider the surface SS defined implicitly by F(x,y,z)=x2+y2−z2−1=0F(x,y,z) = x^2 + y^2 - z^2 - 1 = 0 for z>0z > 0. At the point (2,1,2)(\sqrt{2}, 1, \sqrt{2}), two possible unit normal vectors are n1=13⟨22,2,−22⟩\mathbf{n}_1 = \frac{1}{3}\langle 2\sqrt{2}, 2, -2\sqrt{2} \rangle and n2=13⟨−22,−2,22⟩\mathbf{n}_2 = \frac{1}{3}\langle -2\sqrt{2}, -2, 2\sqrt{2} \rangle. If you want the normal to point away from the z-axis, which normal should you choose?
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