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equation of tangent plane?

Posted 9 years ago

Hi all. What command do I give Mathematica to solve "Find the equation of the tangent plane and the normal line at the point (2,3,2) on the surface 4x^2+3y^2+z^2=47"? Thanks!

POSTED BY: D P
3 Replies
Posted 9 years ago

Thanks for the replies. Much appreciated.

POSTED BY: D P

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POSTED BY: Simon Cadrin

Here's an elegant solution. Near the point {2,3,2}, x^2 can be approximated by 2x, y^2 by 3y and z^2 by 2z. Therefore 4x^2+3y^2+z^2=47 near the point reduces to 8x+9y+2z=47, which is the equation of the tangent plane. To find the normal vector to the plane at {2,3,2}, rewrite the equation for the plane to the form a(x-2)+b{y-3)+c(z-2)=0, The normal vector is then {a,b,c}.

POSTED BY: S M Blinder
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