1. Notes: 8-1 Geometric Vectors
vector: A quantity that has both magnitude and direction. A vector can be represented geometrically by a directed line segment.
water current b o a t
Resultant motion of boat

2. Notes: continued…
magnitude: How fast an object is moving or how much force is being applied to the object. Represented geometrically according to the length of the given line segment.
direction: Represented geometrically according to the angle between the positive x-axis and the vector.

3. Notes: 8-2 Algebraic Vectors
initial point
terminal point 1. 2.

4. The magnitude is zero and it can go in any direction.
Notes: continued… 4.
Opposite vectors
Same magnitude (length), but opposite directions that differ by 180 degrees 3.
zero vector
The magnitude is zero and it can go in any direction.
Both the initial point and terminal point are at the origin.

5. This is the distance formula… a form of the Pythagorean Theorem.
Notes: continued…
5. Vector representation:
Magnitude:
This is the distance formula…
a form of the Pythagorean Theorem.

6. Note: 6. The sum of unit vectors in 2 dimensions:
Notes: continued…
6. The sum of unit vectors
in 2 dimensions:
Note: