We will come up with first the vector form of the equation of a plane, and then expand to get the component form of the equation of a plane. The formula is based on knowing:
1) A point on the plane
2) A normal vector to the plane
Planes are foundational objects in multivariable calculus (for instance, the analog of a tangent line for functions of one variable will be a tangent plane for functions in two variable).
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