How to Find the Unit Tangent, Normal, and Binormal Vectors (Calc 3 Examples)

In this Calculus 3 video, we review how to find the unit tangent, normal, and binormal vectors and work through several example problems step by step. This is a practice-focused continuation of the Frenet frame, with minimal theory and lots of computation. We also apply the TNB frame to find equations of planes associated with space curves. If you’re looking for the full geometric derivation and motivation behind the TNB frame, see the original lecture linked here:    • Calculus 3: Arc Length and Curvature (Vide...   Topics covered: – Unit tangent vector – Unit normal vector – Binormal vector – Why the binormal vector is already a unit vector – Osculating plane examples ▶️ Watch my full Calculus 3 video lectures here:→    • Calculus 3 Video Lectures   ✨ Need guided notes & exclusive content? Join my Patreon: www.patreon.com/mathwithprofessorv xoxo, Professor V #Calculus3 #Calc3 #VectorCalculus #UnitTangentVector #NormalVector #BinormalVector #TNBFrame #FrenetFrame #OsculatingPlane #MultivariableCalculus #mathwithprofessorv https://linktr.ee/mathwithprofessorv 💡 Support & Exclusive Content 👉 Join my channel for perks:    / @mathwithprofessorv   👉 Become a Patron:   / mathwithprofessorv   Patreon gives you access to exclusive ad-free videos, worksheets, and my full math library. The "Star Pupil Package" tier is only $9.99/month! 📺 Watch Next – Calculus Playlists Full Calculus 3 Video Lectures Playlist:    • Calculus 3 Video Lectures   Full Calculus 1 Video Lectures Playlist:    • Calculus 1 Video Lectures   Full Calculus 2 Integration Playlist:    • Calculus 2 Video Lectures   ✨ Most Helpful Integration Lessons (Calc 2) Integration by parts:    • Calculus 2: Integration by Parts (Video #1...   Tabular Integration:    • Integration by Parts - Tabular Method | Ca...   Trigonometric integrals:    • Calculus 2: Trigonometric Integrals (Video...   Trigonometric Substitution:    • Calculus 2: Trigonometric Substitution (Vi...   Partial Fraction Decomposition:    • Calculus 2: Integration of Rational Functi...   Strategy for Integration:    • Calculus 2: Strategy for Integration (Vide...   Improper Integrals:    • Calculus 2: Improper Integrals (Video #7) ...   📘 Quick Trig Review Before Integrals Unit Circle:    • Trigonometry: Circular Functions (Section ...   Trig Identities:    • Precalculus: Trigonometric Identities (Sec...   Sum & Difference Formulas:    • Precalculus: Sum and Difference Formulas f...   Double & Half-Angle Formulas:    • Precalculus: The Double-Angle and Half-Ang...   🛍️ Shop & Support Merch: https://math-with-professor-v.mysprea... Amazon Influencer Store: https://amazon.com/shop/mathwithprofe... 📲 Stay Connected IG: @mathwithprofessorv TikTok: @mathwithprofessorv This video is copy protected and cannot be downloaded or used in any capacity without my permission.