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3D Coordinate Systems

This video introduces the three-dimensional coordinate system and explains how to find distance in 3D space. These ideas extend the coordinate plane into three dimensions and are essential for working with vectors, lines, and surfaces in Calculus 3. We begin by reviewing how points are represented using ordered triples and how to interpret the x-, y-, and z-axes. Then we develop the distance formula in three dimensions by extending the Pythagorean Theorem. The video includes several worked examples, such as: • Plotting points in 3D space • Interpreting coordinates and axes • Finding the distance between two points in three dimensions • Simplifying square roots in distance calculations This video is ideal for students starting Calculus 3 or Multivariable Calculus, and it provides a foundation for topics like vectors, equations of lines, and surfaces. Topics covered in this video: ★ The 3D coordinate system ★ Ordered triples and spatial orientation ★ Distance between two points in 3D ★ Equations of Spheres ★ Geometric interpretation of distance This lesson pairs well with videos on vectors in 3D, dot product, and equations of lines in space. 00:00 Introduction 00:16 Th Big Idea 00:40 Points in 3D Space 01:10 3D Distance Formula 05:02 Distance Using Vectors 05:30 Simple Planes in 3D 06:32 Marker 1 06:51 Equation of a Sphere 07:37 Example 1 08:37 Example 2 11:14 Example 3 13:12 Example 4 14:23 Summary