1. 6.3 Vectors in the plane Day 1 Objectives: - define vectors
- identify component form of a vector
- calculate the magnitude of a vector
Warm Up
Find the distance between the following two points
(5 , 1) & (-2 , 6)

2. Vectors in the plane Definition:
A vector is a quantity possessing magnitude AND direction
Examples:
Velocity, acceleration, magnetic fields, force, etc.
A scalar is a quantity with only magnitude
i.e. Speed vs. Velocity

3. Vectors in the plane
Vectors are usually visualized as a directed line segment or ray on a coordinate plane.
It’s direction goes from an initial point to a terminal point.

4. Vectors in the plane
Note: a vector in standard position has its initial point at the origin.

5. Vectors in the plane
The component form of a vector PQ with initial point (p1 , p2) and terminal point (q1 , q2) is
< q1 - p1 , q2 - p2 > which can also be written
as < v1 , v2 >
Which can also be written as v or

6. Vectors in the plane A vectors magnitude is its length
The magnitude of a vector is denoted by

7. Vectors in the plane
The magnitude of a vector is
Which also equals

8. Vectors in the plane
If = 1, then we call the vector a unit vector ( kind of like the unit circle has radius = 1)

9. Vectors in the plane Example 1:
Find the component form and magnitude of if its initial side is P(3 , -5) and terminal side Q(-2, 7)

10. HOMEWORK
P. 453 # 3-13 ODD