Topic 5 - Vectors (HL Math)
(A) List of Topics and Content to be Taught
point to consider ==> present in the context of familiar concept ==> co-ordinate geometry (i.e Chapter 7 in the textbook) . Then introduce the concept of a vector as related to what we have seen in co-ordinate geometry - a directed line segment. Then we can also introduce vectors in the geometric sense, using figures like parallelograms, rectangles and vectors would simply represent a route for getting from one vertex (point) to another.
| Objective | Topic | Content | Teaching Emphasis |
| 5.1
4 lessons 15(A - I) cover vector basics in 2D and 3D |
Vector Concepts | - representations of vectors | present both an algebraic and geometric
approach (simultaneously) when introducing
these concepts
present vectors as displacements |
| - vector components | |||
| - columnar representation | |||
| - vector addition | |||
| - vector subtraction | |||
| - multiplication by scalars | |||
| - magnitude of a vector | |||
| - unit vectors; base vectors i,j,k | |||
| - position vectors | |||
| 5.2
2 lessons 15(J) - include projections |
Scalar Product of Vectors | - finding scalar products | - focus on applications word problems like motion |
| - algebraic properties of the scalar product | |||
| -applying to parallel and perpendicular vectors | |||
| - finding angle between vectors | |||
| 5.3
2 lessons 17(A,B) |
Vector Form of Linear Equations | - vector form as r = a+ tb and meanings of each | - emphasis applications to motion |
| - the angle between two lines | |||
| 5.4
2 lessons 17(C) |
Intersection of Lines | - finding intersection points | - present in 2-space and 3-space |
| - classifying linear systems as lines being coincident, parallel, intersecting, and skew | |||
| 5.5
2 lessons 15(K) |
Vector Products | - calculation of vector product including representation of the determinant | |
| Geometric Interpretation - Application as areas of triangles and parallelogram | |||
| 5.6
2 lessons 17(D) |
Equations of Planes | - vector equations of planes | |
| - scalar equation of planes | |||
| 5.7
2 lessons 17(EF) |
Intersections | - line with a plane, 2 planes, 3 planes | - show use of row reduction operations |
| - angle between line and plane, and between 2 planes |
(B) Timing/Pacing
From our list of required content, we can now set up a tentative schedule for Topic 5. Note the recommended time frame is 22 hours (or 16.5 classes of 1.3333 hours - 80 minutes).
(C) Sequence of Topics
The relevant sections in the textbook are as follows:
Chapter 15 - Vectors in 2 and 3 Dimensions (9 Classes)
(A) - Vectors
(B) - Operations with Vectors
(C) - 2D Vectors in Component Form
(D) - 3D Co-ordinate Geometry
(E) - 3D Vectors in Component Form
(F) - Algebraic Operations with Vectors
(G) - Vectors in Co-ordinate Geometry
(H) - Parallelism
(I) - Unit Vectors
(J) - Scalar Product of 2 Vectors
(K) - Scalar Product of 2 Vectors
Chapter 17 - Lines in the Plane and in Space (7 days)
(A) - Lines in a Plane and in Space
(B) - Applications of a Line in Space
(C) - Relationship between Lines
(D) - Planes and Distances
(E) - Angles in Space
(F) - Intersection of 2 or more Planes
(D) Schedule