Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Multivariable Calculus
Tangent Planes
Normal Lines
Partial Derivatives
Gradient Vectors

Formulas

Tangent Plane Equation: Fx(x0, y0, z0)(x - x0) + Fy(x0, y0, z0)(y - y0) + Fz(x0, y0, z0)(z - z0) = 0
Normal Line Equation: Parametric form r(t) = (x0, y0, z0) + t(gradF)

Theorems

Gradient Vector Theorem

Suitable Grade Level

College/University Level (Multivariable Calculus)