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### Section 3-2 : Gradient Vector, Tangent Planes and Normal Lines

1. Find the tangent plane and normal line to $$z\,y + 4x\sqrt z - {x^3}{y^2} = 221$$ at $$\left( { - 2,5,9} \right)$$.
2. Find the tangent plane and normal line to $$\displaystyle {{\bf{e}}^{x\,{y^{\,2}}}} + z{y^4} = 61 + \frac{{{z^2}}}{{x + 1}}$$ at $$\left( {0, - 2,6} \right)$$.
3. Find the tangent plane and normal line to $$9yz - \sqrt {{x^2} - 8z} = x{y^2} - 26$$ at $$\left( {3,1, - 2} \right)$$.
4. Find the point(s) on $$6{x^2} + {y^2} - 3{z^2} = 4$$ where the tangent plane to the surface is parallel to the plane given by $$2x + 7y - z = 6$$.
5. Find the point(s) on $${x^2} - 8{y^2} - 2{z^2} = - 3$$ where the tangent plane to the surface is parallel to the plane given by $$- 4x - y + 8z = 1$$.