of 13 /13
13.7 Tangent Planes and Normal Lines for an animation of this topic visit http://www.math.umn.edu/~rogness/multivar/tanplane_withvec tors.shtml

# 13.7 Tangent Planes and Normal Lines for an animation of this topic visit rogness/multivar/tanplane_withvectors.shtml

Tags:

Embed Size (px)

### Text of 13.7 Tangent Planes and Normal Lines for an animation of this topic visit...

13.7 Tangent Planes and Normal Linesfor an animation of this topic visit

http://www.math.umn.edu/~rogness/multivar/tanplane_withvectors.shtml

Recall from chapter 11: • Standard equation of a plane in Space• a(x-x1) + b(y-y1) + c (z – z1) = 0• parametric form equations of a line in

space: x = x1 + at

y = y1 +bt

z = z1 +ct• symmetric form of the equations of a line

in space• x-x1 = y – y1 = z – z1

• a b c

Example 1

For the function f(x,y,z) describe the level surfaces when f(x,y,z) = 0,4 and 10

Example 1 solutionFor the function f(x,y,z) describe the level surface

when f(x,y,z) = 0,4 and 10

For animated normal vectors visit:http://www.math.umn.edu/~rogness/math2374/paraboloid_normals.htmlORhttp://www.math.umn.edu/~rogness/multivar/conenormal.html

Example 2

Find an equation of the tangent plane to given the hyperboloid at the point (1,-1,4)

Example 2 Solution:

Example 3

Find the equation of the tangent to the given paraboloid at the point (1,1,1/2)

Example 3 Solution: Find the equation of the tangent to the given paraboloid at the point (1,1,1/2). Rewrite the function as f(x,y,z) = - z

Example 4

Find a set of symmetric equations for the normal line to the surface given by

xyz = 12

At the point (2,-2,-3)

Example 4 SolutionFind a set of symmetric equations for the normal

line to the surface given by

xyz = 12 At the point (2,-2,-3)

One day in my math class, one of my students spent the entire period standing leaning at about a 30 degree angle from standing up straight. I asked her “Why are you not standing up straight? “

She replied “Sorry, I am not feeling normal.”

Of course that students name was Eileen.

Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents