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How to Find TNB Frames (Frenet-Serret) (Calculus 3 Lesson 33) ➡️ Download my FREE Surfaces Cheat Sheets: https://www.jkmathematics.com//surfaces-cheat-sheets 🖥️ Membership Site (community & bonus content): https://www.jkmathematics.com/plus 🌐 My Website: https://www.jkmathematics.com ⭐️ Support Me on Patreon: https://www.patreon.com/JKMath In this video you will learn about TNB frames, also known as Frenet-Serret frames, and how to find them. TNB frames are composed of 3 vectors: the unit tangent vector, the unit normal vector, and the unit binormal vector. Together, these three vectors describe the heading, turning, and twisting of a particle moving along a path of motion (a curve) in 3D space. We take a look at the formulas for finding each of these vectors, and how they are related to one another. This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture! Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first! Video Chapters: 0:00 What are TNB frames? 10:56 How to Find TNB frames 22:45 Summary of Formulas 25:30 Example Part 1: Finding Unit Tangent Vector 27:55 Example Part 2: Finding Unit Normal Vector 31:28 Example Part 3: Finding Unit Binormal Vector 38:30 Relationship to Curvature 📝 Examples Video: https://www.youtube.com/watch?v=BnbM0iZNY3M ⏩ Next Lesson: 📺 Calculus 3 Playlist: https://www.youtube.com/playlist?list=PLHdRLeAbIZE5yZ7ydR9qeB_B6CcVFlX63 📺 Calculus 2 Playlist: https://www.youtube.com/playlist?list=PLHdRLeAbIZE7KQ922piyRIDAj30XYcOIu 📺 Calculus 1 Playlist: https://www.youtube.com/playlist?list=PLHdRLeAbIZE6krGDQthaQRpLZFLD4ob54 ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://www.amazon.com/Texas-Instruments-TI-Nspire-Graphing-Calculator/dp/B07RL7HM5V?language=en_US Non-Graphing Calculator: https://www.amazon.com/Texas-Instruments-TI-30X-Scientific-Calculator/dp/B00SWWKEAY?language=en_US Financial Calculator: https://www.amazon.com/s?k=ba+2+plus&language=en_US Graphing Paper: https://www.amazon.com/KAISA-Punched-Loose-Leaf-Binders-150sheet/dp/B096V2RYR2?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&language=en_US College Rule Paper: https://www.amazon.com/Mead-Filler-College-Punched-15326/dp/B000068UWB?language=en_US My Favorite Pencil: https://www.amazon.com/Quick-Mechanical-Pencil-Assorted-Barrel/dp/B07FC5NGBX?language=en_US My Favorite Erasers: https://www.amazon.com/Prismacolor-Premier-Magic-Erasers-3-Count/dp/B005ENNEJW?language=en_US Calculus Workbook: https://www.amazon.com/Essential-Calculus-Practice-Workbook-Solutions/dp/1941691242?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&language=en_US ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://www.amazon.com/Calculus-Ron-Larson/dp/0547167024?language=en_US Calculus 3: https://www.amazon.com/Multivariable-Calculus-Ron-Larson/dp/1285060296?language=en_US Financial Mathematics: https://www.amazon.com/Mathematics-Investment-Credit-ACTEX-Academic/dp/1566987679?language=en_US Algebra: https://www.amazon.com/Beginning-Algebra-Textbooks-Available-Cengage/dp/1111578702?dib=eyJ2IjoiMSJ9.g0T1GWGzoYKWtGxkj7UalJvCBFYIbNvNGfdeC55goiBg0R4T5OKmBFctoPC2aiQ6TGMfZ0Hgm0kD7yJwMG1IBxaNXWVuU5E8_Z8jzEYNMPoECwTXdNPKeaJHdi6k0nGpwFtaSkDxDCS9ubXCek9laEQflYsOhMfPCarQ6gQPcgAKeyHc79eTbeNCdhsHqz7aRL0gWNzoNN2oMi-fPo9sJ2AMQULppYXjBdAJHry93bCOmjCocOZrI1shLqCMNrQI6eiZUjcHtAALs9aKh21e4IUjdtRa3_3RW8Sg9AJHeyZwUkDBTTtfDvdbvWLDxcYg2vXkdezLVf1Ciixo_feMSNh7oD6w--Iu-TnWEyjxS_2qXvTsTWEN4pQIPq7gZIC26Ncag297fdhehj8oKpt-0bkc1_H1HX8YugHTGDWo4pc7gGIU6IoP1LXDwKlDJRF_.9PoBEP5UOvzmv0NibJkKbRZFnddOsK25HxJ-cGrUg8o&dib_tag=se&language=en_US ⚡️My Recording Equipment⚡️ iPad Air: https://www.amazon.com/Apple-iPad-Air-5th-Generation/dp/B09V3HJBN3?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&th=1&language=en_US Apple Pencil (Gen 2): https://www.amazon.com/Apple-MU8F2AM-A-Pencil-Generation/dp/B07K1WWBJK?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&language=en_US Tablet Desk Stand: https://www.amazon.com/OMOTON-Adjustable-Multi-Angle-Aluminum-Convenient/dp/B015FH0XKE?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&th=1&language=en_US External Hardrive: https://www.amazon.com/Toshiba-HDTB420XK3AA-Canvio-Portable-External/dp/B079D3D8NR?language=en_US (Commissions earned on qualifying purchases) Follow me on Social Media! https://www.facebook.com/unsupportedbrowser Found this video to be helpful? 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