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Equations of Planes

In this video, we introduce equations of planes in three-dimensional space and explain how to work with them in Calculus 3. You’ll learn how vectors help us describe planes algebraically and geometrically. We focus on the geometric meaning behind plane equations and how to build them step by step. Topics covered include: • What a plane is in 3D space • Normal vectors and why they matter • The standard form of a plane equation • Writing the equation of a plane given a point and a normal vector • Interpreting plane equations geometrically This video emphasizes understanding over memorization and sets the foundation for later topics such as intersections of planes, distance to a plane, and applications in physics and engineering. This lesson is ideal for students in Calculus 3, multivariable calculus, or anyone wanting a clear introduction to planes in 3D space. 00:00 Introduction 00:11 The Big Idea 00:57 Point-Norrnal Equation 01:24 Expanede Form 01:46 Standard Form 02:36 Example 1 07:32 Example 2 10:42 Example 3 12:52 Example 4 17:27 Summary and What's Next