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How to Find Equations of Lines in 3D Space (Calculus 3 Lesson 15) ➡️ Download my FREE Vector Cheat Sheets: https://www.jkmathematics.com//vector-cheat-sheets-calc3 🖥️ Join My Membership Site: https://www.jkmathematics.com/plus In this video you will learn how to represent lines in 3D space with symmetric equations and parametric equations. You will see where the general form of these equations come from as well as how to use them to represent lines in 3D space using a point on that line and a vector parallel to it (direction vector). Additionally, you will see plenty of examples showing you how to represent lines in 3D space using the equations. 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 2D vs 3D Lines: What’s the Difference? 3:04 Finding Formulas for Lines in 3D 15:22 Symmetric & Parametric Equations of Lines in 3D 16:21 Example: Finding Equations of Lines in 3D (#1) 22:02 Example: Finding Equations of Lines in 3D (#2) 28:45 Example: Finding Point on Line & Parallel Vector (Parametric) 31:23 Example: Finding Point on Line & Parallel Vector (Symmetric) 34:26 Direction Numbers = 0? 39:10 Example: Line Equations with Direction Number = 0 44:07 Example: Parallel Lines in 3D? 📝 Examples Video: https://www.youtube.com/watch?v=l_4KDFc6Hkw ⏩ Next Lesson: https://www.youtube.com/watch?v=C6tMbe-ZmCM 📺 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 🌐 Visit My Website: https://www.jkmathematics.com ⚡️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 ⚡️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) Find me on social media: ➡️ Facebook: https://www.facebook.com/unsupportedbrowser ➡️ Twitter: https://twitter.com/jk_mathematics ➡️ Instagram: @jk_mathematics Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! - Josh from JK Mathematics #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.