This document provides an overview of vectors in a plane including: 1) Ways to represent vectors in component form, linear form, and trigonometric form. 2) How to perform vector operations such as addition, subtraction, and scalar multiplication both graphically and algebraically. 3) Examples of finding vectors between two points, writing vectors as linear combinations of standard unit vectors, graphing vector operations, and converting between component form and trigonometric form.

1. 6.3 Vectors in a Plane
Objective:
1) Perform operations with vectors, both
graphically and algebraically.
2) Apply vectors in real-life situations.
Standard: Linear Algebra 7.0

2. What's a
Vector?
_____________
_____________
It's got _________ and _____________!
Terminal – Initial

3. Ways to represent vectors:
Component Form:
Linear Form:
Trigonometric Form:

4. On the Moodle Discussions:
Don't use < and > for vectors. Use LaTeX.
$$langle{-3,5}rangle$$
$$|v|$$

5. Finding a vector:
Ex. 1) Find the component form and
magnitude of the vector v that has an
initial point of (–2, 3) and terminal point
(–7, 9).

6. Ex. 2) Let u be the vector with initial point
(–2, 6) and terminal point (–8, 3). Write u
as a linear combination of the standard
unit vectors i and j.

7. Vector Operations:
Ex. 3) Find the following if …
a) u–v
b) 3v–2u

8. Graphing Vectors:
Ex. 3b) Graph the following if …
a) u+v
b) 3v–2u

9. Ex. 4) Let u = i + j and v = 5i - 3j. Find
3u - 2v.

10. Direction Angles
Ex. 5) Find the direction angle.
a) -6i+6j
b)

11. Trigonometric Form
Just like _____, ______, and ______ can
be used to represent a location on a plane,
also _____, _____, and _____________
can be used in the same way.
Ex. 6) Write in trig form.

12. Assignment:
#8 p. 456 #3-13
(odd), 21-33
(odd), 45-66
(mult. of 3)