YouTube - Video notes - Video sections playlist - Vectors and the Geometry of Space playlist
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: 35:07
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
Vectors and the Geometry of Space: Problems Plus