1. 13.7 day 2 Tangent Planes and Normal Lines

2. Example 5
Describe the tangent line to the curve of intersection of the given surfaces at the point (0,1,3) (see diagram)
(0,1,3)

3. Example 5 Solution

4. Angle of Inclination of a plane
Recall the angle between two planes is given by:
The angle of inclination of a plane is given by:
(using the normal vectors)
Note: n is a normal vector to the plane
k is the vector in the z direction

5. Example 6
Find the angle of inclination of the tangent plane to the ellipsoid given by:
at (2,2,1)
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6. Solution to example 6 (slide 1)

7. Recall from yesterday:

8. Problem 54
Find the point at which the tangent plane is horizontal