1. Vectors in the Plane

2. Example of equivalent vectors

3. Example 1
Let v be represented by the directed line segment from (0,0) to (3,2); and let u be the directed line segment from (1,2) to (4,4) show that u and v are equivalent.

4. Example 1 solution Solution
Let P(0,0) and Q(3,2) be the initial and terminal points of v
and let R(1,2) and S(4,4) be the initial and terminal points of u.
You can use the distance formula to show that PQ and RS have the same length (magnitude) → →
The two vectors are in the same direction because they have the same slope
If two vectors have the same magnitude and direction,
they are said to be equivalent vectors

6. Example 2
Find the component form of the vector v that has initial point (3,-7) and terminal point (-2,5)

7. Example 2 solution
Find the component form of the vector v that has initial point (3,-7) and terminal point (-2,5)

8. Definitions of Vector Addition and Scalar Multiplication

9. Graphic examples of scalar multiplication

10. Graphing representation of adding vectors

11. Graphing representation of vector operations

16. On the TI 89 type in (in degree mode)
rref([cos 30,cos130, 0; sin30,sin130,2000])

17. Examples
P. 771
Do examples 24,34,56,82 from text