13.7 day 2 Tangent Planes and Normal Lines

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Presentation transcript:

13.7 day 2 Tangent Planes and Normal Lines

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)

Example 5 Solution

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

Example 6 Find the angle of inclination of the tangent plane to the ellipsoid given by: at (2,2,1) ___ 3

Solution to example 6 (slide 1)

Recall from yesterday:

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