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## Homework Statement

Check that the point (-1,1,2) lies on the given surface. Then find a vector normal to the surface and an equation for the tangent plane to the surface at (-1,1,2).

z=x

^{2}+ y

^{2}

## Homework Equations

## The Attempt at a Solution

(2) = (-1)

^{2}+ (1)

^{2}

2 = 2; (-1, 1, 2) lies on the surface z=x

^{2}+ y

^{2}

----------

0 = -z + x

^{2}+ y

^{2}

f(x,y,z) = -z + x

^{2}+ y

^{2}

∇f = <2x, 2y, -1>

∇f (-1,1,2) = <-2,2,-1>

tangent plane: -2(x+1) + 2(y-1) - (z-2) = 0

-2x + -2 + 2y - 2 - z + 2 = 0

-2x + 2y - z = 2 <------- Tangent plane equation

normal line: < -2, 2, -1>

as unit vector: (1/√3) <-2, 2, -1>

Did I do this correctly?