Name: Vectors and the Geometry of Space: Problems Plus
Uploaded: 2024-10-01T05:20:19+00:00
Duration: 4 h 12 min 17 s
Description: 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, v

1 year ago

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Health & Science Education math calculus 3D lines planes parallel lines vectors geometry vector geometry

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