Vectors and the Geometry of Space: Review of Chapter

In this video I go over the end of chapter review questions covering the Vectors and the Geometry of Space chapter. There are 19 questions in total and serve as a good review on vectors, dot products, cross products, as well as the equations of lines, planes, and their applications. I also cover a few details, notably the distance between a point and a line, differently than I had in my earlier videos covering the chapter; so make sure to watch this video!

The topics covered as well as their timestamps are listed below.

• Intro: 0:00
• Calculus Book Reference: 0:58
• Sections in Calculus Book Chapter: 1:14
• Topics to Cover: 1:57
• Review: Concept Check: 19 Questions: 2:19

1. Question 1: Vector vs scalar: 2:54
2. Question 2: Vector addition: 3:33
3. Question 3: Multiplying vector by a scalar: 6:14
4. Question 4: Position vector: 7:45
5. Question 5: Dot product: 9:20
6. Question 6: Applications of dot product: 11:20
7. Question 7: Scalar and vector projections: 19:05
8. Question 8: Cross product: 21:02
9. Question 9: Applications of cross product: 27:33
10. Question 10: Parallelogram and Parallelepiped: 32:44
11. Question 11: Vector perpendicular to plane: 34:28
12. Question 12: Angle between 2 planes: 35:48
13. Question 13: Vector, parametric, and symmetric equations for a line: 37:04
14. Question 14: Vector and scalar equation for a plane: 40:46
15. Question 15: Parallel or perpendicular vectors and planes: 42:41
16. Question 16: Points on a line or plane: 46:22
    • Solution to (a): 3 Points on a Line: 46:40
    • Solution to (b): 4 Points on a Plane: 49:56
17. Question 17: Distances between Points, Lines, Planes: 52:08
    • Solution to (a): Distance from a Point to a Line: 52:30
    • Solution to (b): Distance from a Point to a Plane: 58:21
    • Solution to (c): Distance between Two Lines: 1:00:00
18. Question 18: Traces of a surface: 1:14:50
19. Question 19: Six types of quadric surfaces: 1:21:58

• Outro: 1:26:53

Video notes and playlists:

• PDF notes: https://1drv.ms/b/s!As32ynv0LoaIi4Bu972HIENqNtdhRg
• HIVE notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-review
• Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EMiATrjv8HH3fPwKVsgU6P
• Vectors and the Geometry of Space playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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