Find equation of the tangent plane

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To find the equation of the tangent plane to the level surface defined by the scalar field ξ(x,y,z) = x² + y² + z² at the point (1,1,2), one must first determine the gradient of the function at that point. The gradient, which is a vector of partial derivatives, provides the normal vector to the tangent plane. The general equation of a plane can then be used, incorporating the normal vector and the coordinates of the point. The tangent plane serves as a linear approximation of the function around the specified point. This approach allows for the precise formulation of the tangent plane equation.
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Find the equation of the tangent plane to the level surface of the scalar field

\xi(x,y,z) = x2+y2+z2

at the point (1,1,2)




Looking the work through this question with someone, not to sure where to start.
 
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i would start with the general equation of a plane...

the tangent plane can be thought of as a linear approximation of the function at that point
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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