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A normal vector to the implicitly defined surface $g(x,y,z) = c$ is $\nabla g(x,y,z)$. Level curves and surfaces We identify the surface as the level curve of the value $c=3$ for $g(x,y,z) = x^3 +
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M ( x o) = − 1 8. The point slope form of the equation is, ( y − y o) = M ( x − x o) So, the equation of normal line at (1, 4) can be calculated as, ( y − 4) = − 1 8 ( x − 1) y = − x 8 + 1 8
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In the process we will also take a look at a normal line to a surface. Let’s first recall the equation of a plane that contains the point (x0,y0,z0) ( x 0, y 0, z 0) with normal
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