Vectors and the Geometry of Space: Problems Plus

In this video I go over the end-of-chapter Problems Plus advanced math problems for the Vectors and Geometry of Space chapter. There are 8 problems in total and cover 3D geometry, surfaces, vectors, vector projections, and applications to physics and airplane dynamics. It's 4 hours of advanced math so buckle up!

Timestamps:

• Intro: 0:00
• Calculus Book Reference: 0:56
• Sections in Calculus Book Chapter: 1:10
• Topics to Cover: 2:02
• Review: Concept Check: 19 Questions: 2:19

1. Problem 1: Tightly packed balls in a box: 2:22
   • Hint: Use analogy problem solving strategy: 3:32
   • Solution: Solving the 2D case first: 4:51
   • Solving the 3D case: 9:32
2. Problem 2: Volume around a box: 18:25
   • Solution: Solving the 2D case first: 19:07
   • Solving the 3D case: 22:19
3. Problem 3: Intersecting planes: 33:57
   • Solution to (a): Symmetric equations for the line: 34:56
   • Solution to (b): Curve of intersection as c varies: 1:02:13
   • Solution to (c): Volume of hyperboloid surface: 1:23:25
4. Problem 4: Playing flying in wind: 1:27:32
   • Solution to (a): Wind velocity: 1:28:30
   • Solution to (b): Modified plane velocity: 1:39:21
5. Problem 5: Sum of vector projections: 1:50:46
   • Recap on the Geometric series: 2:10:31
6. Problem 6: Largest sphere in a sphere: 2:13:27
7. Problem 7: Block on an inclined plane: 2:41:46
   • Solution to (a): Coefficient of static friction: 2:46:29
   • Solution to (b): Applying a minimal horizontal force: 2:51:16
   • Solution to (c): Minimal horizontal force formula: 3:05:16
   • Solution to (d): Maximum horizontal force: 3:15:47
8. Problem 8: Volume of a solid from its shadows: 3:35:32
   • Solution to (a): Volume of largest such solid: 3:37:24
   • Solution to (b): No smallest volume: 4:08:26

• Outro: 4:11:21

Video notes and playlists:

• PDF notes: https://1drv.ms/b/s!As32ynv0LoaIi6hk12JdmqCKF95B_g
• HIVE notes: https://peakd.com/hive-128780/@mes/jlgigkdl
• Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_7Jd6ZORHFQMk8jbwmkos
• Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join

DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate

SUBSCRIBE via EMAIL: https://mes.fm/subscribe

MES Links: https://mes.fm/links

MES Truth: https://mes.fm/truth
Official Website: https://MES.fm
Hive: https://peakd.com/@mes

Email me: contact@mes.fm

Free Calculators: https://mes.fm/calculators

BMI Calculator: https://bmicalculator.mes.fm
Grade Calculator: https://gradecalculator.mes.fm
Mortgage Calculator: https://mortgagecalculator.mes.fm
Percentage Calculator: https://percentagecalculator.mes.fm

Free Online Tools: https://mes.fm/tools

iPhone and Android Apps: https://mes.fm/mobile-apps