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# Pc8-1 Vectors (part 1)

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### Pc8-1 Vectors (part 1)

1. 2. Geometric Vectors Precalculus 8-1 p. 485
2. 3. Vectors <ul><li>A vector is a quantity that has both magnitude and direction . </li></ul>
3. 4. Vectors <ul><li>A vector is a quantity that has both magnitude and direction . </li></ul><ul><li>A vector is represented geometrically by a directed line segment . </li></ul>
4. 5. Vectors <ul><li>Magnitude: Length of the vector </li></ul><ul><ul><li>For vector a , the magnitude is written | a | </li></ul></ul>
5. 6. Vectors <ul><li>Two vectors are equal  they have the same direction and magnitude </li></ul>
6. 7. Vectors <ul><li>Magnitude: Length of the vector </li></ul><ul><li>Initial: Starting point </li></ul>
7. 8. Vectors <ul><li>Magnitude: Length of the vector </li></ul><ul><li>Initial: Starting point </li></ul><ul><li>Terminal: Ending point </li></ul>
8. 9. Vectors <ul><li>If a vector has its initial point at the origin , it is in standard position. </li></ul>
9. 10. Vectors <ul><li>If a vector has its initial point at the origin, it is in standard position. </li></ul><ul><li>The direction of the vector is the angle between the positive x-axis and the vector. </li></ul>
10. 11. Vectors <ul><li>If both the initial point and the terminal point are at the origin, the vector is the zero vector . </li></ul>
11. 12. Vectors <ul><li>Resultant: The sum of 2 or more vectors. </li></ul><ul><ul><li>Components: The 2 (or more) original vectors. </li></ul></ul>
12. 13. Vectors <ul><li>Resultant: The sum of 2 or more vectors. </li></ul><ul><li>Opposites: Two vectors with the same magnitude and opposite directions. </li></ul><ul><ul><li>Opposite of g is -g </li></ul></ul>
13. 14. Vectors <ul><li>Resultant: The sum of 2 or more vectors. </li></ul><ul><li>Opposites: Two vectors with the same magnitude and opposite directions. </li></ul><ul><li>Scalar: A number with no direction (only magnitude). </li></ul><ul><ul><li>Multiplying a scalar and a vector changes the magnitude of the vector. </li></ul></ul>
14. 15. Vectors <ul><li>Resultant: The sum of 2 or more vectors. </li></ul><ul><li>Opposites: Two vectors with the same magnitude and opposite directions. </li></ul><ul><li>Scalar: A number with no direction (only magnitude). </li></ul>