Calculus

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Vector normal to the tangent plane of a 3D surface.

Diagram of a 3D surface with tangent plane at point P, showing two tangent vectors along intersecting curves and a normal vector orthogonal to the tangent plane.

This diagram illustrates the normal vector to a tangent plane at a point P on a 3D surface S. The tangent plane, depicted in light gray, contains two tangent vectors v1​ and v2​ along the curves C1 and C2​ that intersect at P. The normal vector n is shown perpendicular to the tangent plane, representing the direction orthogonal to both vectors v1​ and v2​.

This visual helps students in multivariable calculus and differential geometry understand the concept of tangent planes, normal vectors, and directional derivatives.

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