## Question

###### Determine whether the following statements are true and give an explanation or counterexample. a. Suppose you are standing at the center of a sphere looking at a point $P$ on the surface of the sphere. Your line of sight to $P$ is orthogonal to the plane tangent to the sphere at $P$. b. At a point that maximizes $f$ on the curve $g(x, y)=0,$ the dot product $\nabla f \cdot \nabla g$ is zero.

Determine whether the following statements are true and give an explanation or counterexample. a. Suppose you are standing at the center of a sphere looking at a point $P$ on the surface of the sphere. Your line of sight to $P$ is orthogonal to the plane tangent to the sphere at $P$. b. At a point that maximizes $f$ on the curve $g(x, y)=0,$ the dot product $\nabla f \cdot \nabla g$ is zero.

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