Three Important Vectors- TNB

🧭 The TNB Frame (Frenet Frame) | Tangent, Normal, and Binormal Vectors | Calculus 3 In this video, we introduce the TNB frame (also called the Frenet frame) for a space curve and explain how the tangent, normal, and binormal vectors work together to describe the geometry of a curve in three dimensions. We’ll cover: What the T, N, and B vectors represent geometrically How the TNB frame moves along a curve The formulas for Unit tangent vector T Unit normal vector N Binormal vector B = T × N Step-by-step examples computing T, N, and B for parameterized curves How to verify that T, N, and B are unit vectors How to show that T, N, and B are mutually orthogonal Common pitfalls and interpretation tips By the end of this video, you’ll understand not just how to compute the TNB frame, but why it works and how it connects to curvature, motion, and the geometry of space curves. 📌 Recommended background: vector-valued functions, derivatives, unit vectors, cross products 📌 Essential for: curvature, Frenet formulas, and motion along curves in Calculus 3 If this video helps, be sure to like, subscribe, and check out the rest of the Calculus 3 playlist! 0:00 Introduction 00:14 The Big Idea 01:36 The Three Vectors and their properties 03:43 Example 1 06:39 Example 2 11:40 Summary