Learning Objectives:

__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

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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