Vector Geometry of Lines and Planes

Learning tasks

A) Vector Geometry of Lines
1) Analyzing Alignment and Relative Positions of Lines	Ex 1 Ex 2 Ex 3 Ex 4 Ex 5
2) Establishing a Parametric Representation of a Line	Ex 6 Ex 7 Ex 8
3) Proving the Alignment of Three Points	Ex 9 Ex 10 Ex 11 Ex 12
4) Determining if a Point Belongs to a Line	Ex 13 Ex 14 Ex 15 Ex 16
5) Determining the Relative Position of Two Lines	Ex 17 Ex 18 Ex 19
6) Proving that Two Lines are Secant	Ex 20 Ex 21
7) Determining the Orthogonality of Two Lines	Ex 22 Ex 23 Ex 24
B) Vector Geometry of Planes
8) Analyzing Coplanarity and Relative Positions	Ex 25 Ex 26 Ex 27 Ex 28 Ex 29
9) Testing the Coplanarity of Four Points	Ex 30 Ex 31
10) Establishing Parametric Equations of a Plane	Ex 32 Ex 33
11) Determining if a Line and a Plane are Parallel	Ex 34 Ex 35
12) Studying Geometric Properties in a Tetrahedron	Ex 36 Ex 37 Ex 38
C) Normal Vectors to a Plane
13) Analyzing Normal Vectors and Plane Perpendicularity	Ex 39 Ex 40 Ex 41 Ex 42
14) Applying the Properties of Normal Vectors to a Plane	Ex 43 Ex 44 Ex 45 Ex 46
D) Cartesian Equation of a Plane
15) Determining the Cartesian Equation of a Plane	Ex 47 Ex 48 Ex 49 Ex 50
16) Determining the Relative Position of Two Planes	Ex 51 Ex 52 Ex 53
17) Determining the Cartesian Equation of a Plane from Three Points	Ex 54 Ex 55
18) Proving that a Line is Normal to a Plane	Ex 56 Ex 57
19) Studying Parallelism and Angles in Space	Ex 58
E) Distance from a Point to a Plane
20) Understanding Projections and Distances	Ex 59 Ex 60 Ex 61 Ex 62
21) Verifying Orthogonal Projections and Distances	Ex 63 Ex 64
22) Determining the Parametric Representation of a Perpendicular Line	Ex 65 Ex 66 Ex 67
23) Calculating the Coordinates of an Orthogonal Projection	Ex 68 Ex 69 Ex 70 Ex 71
24) Solving a Comprehensive Geometry Problem in Space	Ex 72

Lesson
Text book

Exercises Correction
A) Vector Geometry of Lines
    1) Analyzing Alignment and Relative Positions of Lines Ex 1 Ex 2 Ex 3 Ex 4 Ex 5
    2) Establishing a Parametric Representation of a Line Ex 6 Ex 7 Ex 8
    3) Proving the Alignment of Three Points Ex 9 Ex 10 Ex 11 Ex 12
    4) Determining if a Point Belongs to a Line Ex 13 Ex 14 Ex 15 Ex 16
    5) Determining the Relative Position of Two Lines Ex 17 Ex 18 Ex 19
    6) Proving that Two Lines are Secant Ex 20 Ex 21
    7) Determining the Orthogonality of Two Lines Ex 22 Ex 23 Ex 24
B) Vector Geometry of Planes
    8) Analyzing Coplanarity and Relative Positions Ex 25 Ex 26 Ex 27 Ex 28 Ex 29
    9) Testing the Coplanarity of Four Points Ex 30 Ex 31
    10) Establishing Parametric Equations of a Plane Ex 32 Ex 33
    11) Determining if a Line and a Plane are Parallel Ex 34 Ex 35
    12) Studying Geometric Properties in a Tetrahedron Ex 36 Ex 37 Ex 38
C) Normal Vectors to a Plane
    13) Analyzing Normal Vectors and Plane Perpendicularity Ex 39 Ex 40 Ex 41 Ex 42
    14) Applying the Properties of Normal Vectors to a Plane Ex 43 Ex 44 Ex 45 Ex 46
D) Cartesian Equation of a Plane
    15) Determining the Cartesian Equation of a Plane Ex 47 Ex 48 Ex 49 Ex 50
    16) Determining the Relative Position of Two Planes Ex 51 Ex 52 Ex 53
    17) Determining the Cartesian Equation of a Plane from Three Points Ex 54 Ex 55
    18) Proving that a Line is Normal to a Plane Ex 56 Ex 57
    19) Studying Parallelism and Angles in Space Ex 58
E) Distance from a Point to a Plane
    20) Understanding Projections and Distances Ex 59 Ex 60 Ex 61 Ex 62
    21) Verifying Orthogonal Projections and Distances Ex 63 Ex 64
    22) Determining the Parametric Representation of a Perpendicular Line Ex 65 Ex 66 Ex 67
    23) Calculating the Coordinates of an Orthogonal Projection Ex 68 Ex 69 Ex 70 Ex 71
    24) Solving a Comprehensive Geometry Problem in Space Ex 72