Question

Normal to the surface x2 + y2 + z? = 9 at (1,2,2) is​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Concept

Normal line

Let f(x,y,z) be the surface so the equation of normal to the surface at (a,b,c) is $\frac{x-a}{\frac{df}{dx} } =\frac{y-b}{\frac{df}{dy} } =\frac{z-c}{\frac{df}{dz} }$.

Given

The surface is $x^2 + y^2 + z=9$.

Find

We have to find the normal on the surface at (1,2,2).

Solution

Find the of  $\frac{df}{dx}$ ,$\frac{df}{dy}$ and $\frac{df}{dz}$at (1,2,2).

then

1.   $\frac{df}{dx}=2x$ at (1,2,2) the value is 2.

2.   $\frac{df}{dy}=2y$ at (1,2,2) the value is 4.

3.  $\frac{df}{dz}=1$ at (1,2,2) the value is 1.

substitute these values in standard form of normal line of the surface.

$\frac{x-1}{2 } =\frac{y-2}{4 } =\frac{z-2}{1 }$