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(d) Find the equations of the tangent plane and normal line to the surface 4 = xyz at the point i+2j+2k. -----------------------------------------
(d) Find the equations of the tangent plane and normal line to the surface 4 = xyz at the point  i+2j+2k.

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```
10 years ago Latika Leekha
165 Points
```							Hello student,The equation of surface is F(x, y, z) = xyz – 4 = 0Differentiating this equation partially w.r.t. x, y and z respectively∂F/∂x = yz∂F/∂y = xz∂F/∂z = xyHence, at the point (1, 2, 2) we have∂F/∂x = 4∂F/∂y = 2∂F/∂z = 2Hence, the equation of tangent plane at (1, 2, 2) is(x-1)4 + (y-2)2 + (z-2)2 = 0So, 2x + y+z = 6Equation of normal line at point (1, 2, 2) is(x-1)/4 = (y-2)/2 = (z-2)/2or (x-1)/2= (y-2)/1 = (z-2)/1
```
5 years ago
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