Vectors and the Geometry of Space: Review of Chapter

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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!

Timestamps:

• 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

• Question 1: Vector vs scalar: 2:54

• Question 2: Vector addition: 3:33

• Question 3: Multiplying vector by a scalar: 6:14

• Question 4: Position vector: 7:45

• Question 5: Dot product: 9:20

• Question 6: Applications of dot product: 11:20

• Question 7: Scalar and vector projections: 19:05

• Question 8: Cross product: 21:02

• Question 9: Applications of cross product: 27:33

• Question 10: Parallelogram and Parallelepiped: 32:44

• Question 11: Vector perpendicular to plane: 34:28

• Question 12: Angle between 2 planes: 35:48

• Question 13: Vector, parametric, and symmetric equations for a line: 37:04

• Question 14: Vector and scalar equation for a plane: 40:46

• Question 15: Parallel or perpendicular vectors and planes: 42:41

• 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

• 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

• Question 18: Traces of a surface: 1:14:50

• Question 19: Six types of quadric surfaces: 1:21:58

• Outro: 1:26:53