Unit 5: Representing Vectors
MVC4U
Lesson Outline
Big Picture
Students will:
 introduce vectors in two-space and three-space;
 represent vectors geometrically and algebraically;
 determine vector operations and properties;
 solve problems involving vectors, including those arising from real-world applications.
Day
Lesson Title
1 Calculus and Vector 
Connections
2
(lesson not included)
Vectors in Two
Space
(lesson not included)
3
4
5
6
7
8
9
Going from
Geometric to
Algebraic



Math Learning Goals
Explore connections between calculus and vectors.
Expectations
C1.1
Represent vectors geometrically and algebraically in twospace.
Develop an understanding of equivalent vectors.
Use geometric vectors to interpret information arising from
real-world applications (Use applets described in
Appendix A.).
C1.1, 1.2
Determine methods for changing from geometric (directedline segment) to algebraic (Cartesian) forms of a vector in
two-space and vice versa.
C1.3
(lesson not included)
Vector Operations

Add, subtract, and multiply vectors by a scalar in two-space, C2.1, 2.3
both geometrically and algebraically.
(lesson not included)  Solve problems including problems arising from real-world
applications involving vector operations in two-space.
Dot Products in
C2.4
 Determine the dot product of vectors in two-space
Two-Space
geometrically and algebraically.
 Describe applications in two-space of the dot-product
(lesson not included)
including projections.
Jazz Day
(Use applets described in Appendix A.)
Summative
Assessment
Vectors in ThreeC1.4, 2.1, 2.3
 Represent both points and vectors algebraically in threeSpace
space.
 Determine the distance between points and the magnitude of
(lesson not included)
vectors in three-space both geometrically and algebraically.
 Solve problems including problems arising from real-world
applications involving vector operations in three-space.
Investigating
 Investigate, with and without technology, the commutative, C2.2
Properties of
associative and distributive properties of the operations of
Operations
addition, subtraction, and multiplication by a scalar in two
and three-space (Use Vector Laws applet described in
(lesson not included)
Appendix A.).
TIPS4RM: MCV4U: Unit 5 – Representing Vectors
2008
1
Day
Lesson Title
10 Dot Products in
Three-Space
(lesson not included)
11
Investigating
Properties of Dot
Products
Math Learning Goals



Determine the dot product of vectors in three-space
geometrically and algebraically.
Describe applications in three-space of the dot-product
including projections.
Determine through investigation the properties of dot
product in two-and three-space.
Expectations
C2.4
C2.5
12
(lesson not included)
Three-Space Cross 
Products
C2.6
Determine the cross product of vectors in three-space
algebraically including magnitude and describe applications.
13
(lesson not included)
Properties of Cross 
Products
Through investigation, determine properties of the cross
product of vectors.
C2.7
14
(lesson not included)
Applications of

Vector Operation
Solve problems arising from real-world applications that
involve the use of dot products, cross products, including
projections.
C2.8
15
16
(lesson not included)
Jazz Day
Summative
Assessment
TIPS4RM: MCV4U: Unit 5 – Representing Vectors
2008
2