Transcript Section 13.7

Section 13.7
Tangent Planes and Normal Lines
Definition of Tangent Plane and
Normal Line
• Find an equation of the tangent plane to the
surface at the indicated point.
x  y  z  36
2
2
2
(2, -2, 4)
If the surface is given by z=f(x,y)
you can define the function F by
F(x,y,z)=f(x,y) – z
Then the equation of the tangent
plane is given by
f x ( x0 , y0 )( x  x0 )  f y ( x0 , y0 )( y  y0 )  ( z  z0 )  0
The angle of inclination of a plane
is defined to be the acute angle
between the given plane and the
xy-plane,
 
 
nk
nk
cos      
n
n k