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Students often memorize projection formulas without ever really understanding what scalar projection, vector projection, and orthogonal projection mean. In this video, we build the ideas from geometry first — starting with vector components, then generalizing projections to arbitrary directions, and finally explaining how projections are used in distance problems. This explanation is especially helpful for students in Linear Algebra, Multivariable Calculus (Calculus 3), and Vector Calculus. 📌 If you’re currently taking Calculus 3, I have full-length video lectures that walk through these concepts step-by-step with worked examples. You can find those linked below. Topics covered: – Scalar projection vs vector projection – Orthogonal projection and vector decomposition – Conceptual interpretation of projection formulas – Why projections appear in distance problems ▶️ 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 #LinearAlgebra #VectorProjection #ScalarProjection #OrthogonalProjection #Calculus3 #MultivariableCalculus #VectorCalculus #MathWithProfessorV #ConceptualMath 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. #mathwithprofessorv #integration #partialfractions #trigonometricsubstitution #trigintegrals #integrals #integralcalculus #calculus2 #calculusvideos #integralvideos #trigonometricintegrals #math #youtubemath #mathvideos #mathtutor #mathprofessor #integrationbyparts #calculuspractice #calc2review #integralpractice