1. Chapter 6
6.3 – 6.5
Vectors

2. 6.3 Vectors in the Plane Component Form of a Vector
Vectors have an Initial Point and a Terminal Point.
They travel in a direction. LABELS: u, v, w or
To have equivalent vectors, you must have the same slope and the same magnitude. Magnitude is the length.
Component Form of a Vector
v – Standard Position
Initial Pt. (0, 0) to Terminal Pt.
v =
Magnitude =
Magnitude=1, Unit Vector
Given 2 points, Find Component Form
Magnitude???

3. 6.3 cont’d. Example: Find Component Form and Magnitude of
Basic Vector Operations
Given:
Finding Unit Vectors:
Find: 2v
w – v
v + 2w
3w – 5v
Length = 1, Example
Standard Unit Vectors
Is the same as:
EXAMPLES…….

4. 6.4 Vectors and Dot Products
Properties p.422, please look at them!!!!!
Examples, find the Dot Product
Given:
Magnitude =
Find:
Angle between 2 vectors
Vectors are orthogonal if dot product is zero.
Parallel????
Find angle btwn

5. 6.5 Trig. Form of a Complex Number
Complex plane – real axis and imaginary axis
Absolute Value of a complex number is its length.
Example: Plot -2 +5i and find its absolute value.
Trigonometric Form:
is the same as
r is the modulus of z and
is the argument of z.
Where:
go to Trig Form
go to Complex Form
Examples:
Properties p. 434, if you need them I will give them to you.