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Check if I did this problem correctly please

  • #1

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=x2 + y2


Homework Equations





The Attempt at a Solution



(2) = (-1)2 + (1)2

2 = 2; (-1, 1, 2) lies on the surface z=x2 + y2

----------

0 = -z + x2 + y2
f(x,y,z) = -z + x2 + y2

∇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?
 

Answers and Replies

  • #2
329
34
It looks right to me.
 
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