Calculus 3 Lesson 51: Tangent Planes & Normal Lines

Oct 13, 2025

Hi there! Today I have released Lesson 51 of my Calculus 3 series. In this lesson we learn how to find tangent planes and normal lines at points on surfaces!

In particular you will learn about:

  1. How to use the gradient to find a normal vector to a point on a surface
  2. How to find an equation of a tangent plane and normal line at a point on a surface
  3. How to find the angle of inclination for a tangent plane

I hope you enjoy this new lesson for Calculus 3. Next time we will look at extrema for surfaces in 3D!

Until then,

- Josh

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