Normal Vectors and Tangent Planes to Functions of Two Variables

Tutoring on Normal Vectors and Tangent Planes to Functions of Two Variables

Learning Objectives:

Understand and Apply Normal Vectors and Tangent Planes to Function of Two Variables.

Math Tutoring on Normal Vectors and Tangent Planes to Functions of Two Variables

Unit Normal Vectors to Functions of Two Variables:

If , then the Unit Normal Vector to  is defined by

The Equation of a Tangent Plane of Two Variables in Math Tutoring:

We can define a surface implicitly by . If F is differentiable at , then we can determine an equation of a Tangent Plane to the surface given by  at  by

Because  is normal to the Tangent Plane at , it must be orthogonal to every vector in the Tangent Plane, and we have,

 

 

 

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Hook Questions:

1.    State Normal Vector to functions of two variables?

2.    State Tangent Planes to functions of two variables?

 

 

 

 

 

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