# Trigonometry/Collection of Problems/Vectors
## Identifying Vectors

Which of the following are vector quantities?
| 1. | 4 miles northwest |
| 2. | 5 meters |
| 3. | 1200 people |
| 4. | 10 kilograms |
| 5. | Pulling a cord straight down with a pressure of 10 pounds |
| 6. | $200 |
Given ${\overrightarrow {AB}}$, ${\overrightarrow {CD}}$, ${\overrightarrow {EF}}$, draw the following:
| 7. | ${\overrightarrow {GH}}={\overrightarrow {AB}}$ |
| 8. | ${\overrightarrow {IJ}}=-{\overrightarrow {AB}}$ |
| 9. | ${\overrightarrow {KL}}={\overrightarrow {CD}}$ |
| 10. | $-{\overrightarrow {MN}}={\overrightarrow {CD}}$ |
| 11. | ${\overrightarrow {OP}}=-{\overrightarrow {EF}}$ |
| 12. | ${\overrightarrow {QR}}={\overrightarrow {EF}}$ |
Given the rectangle $ABCD$, study the directions of the vectors, then indicate which statements are true and which are false:
| 13. | ${\overrightarrow {AD}}={\overrightarrow {BC}}$ |
| 14. | ${\overrightarrow {OD}}=-{\overrightarrow {BO}}$ |
| 15. | ${\overrightarrow {AB}}={\overrightarrow {CD}}$ |
| 16. | ${\overrightarrow {AO}}=-{\overrightarrow {OC}}$ |
* 17. Using these two triangles we are given
* ${\overrightarrow {CA}}={\overrightarrow {DF}}$
* and
* ${\overrightarrow {CB}}={\overrightarrow {DE}}$
* Show that ${\overrightarrow {BA}}={\overrightarrow {EF}}$
* Planes A, B, and C leave airport O at 8 A.M., plane A traveling N $60^{\circ }$ E at 600 kilometers per hour, plane B traveling due
* north at 300 kilometers per hour, and plane C traveling southwest at 400 kilometers per hour. On paper or in drawing software, locate a point
* representing the airport O. Through this point draw lines representing an east-west direction and a north-south direction, then sketch vectors
* indicating the change in position of each of the first planes after the first hour of flight. Show correct scale by using 1 cm to represent 100 kilometers.

## Adding Vectors

| 1. | Two forces, one of 300 N and the other of 200 N, act at a point on a body, and are perpendicular to each other. |
| | Construct (on paper or using software) the vector representing the sum of the two forces. |
| 2. | Construct the vector representing the sum of the two forces in Exercise 1 when the forces form an angle of $45^{\circ }$ |
| | with each other. |
| 3. | Two forces, one of 100 Newtons and one of 175 Newtons, act at a point on a body, and form an angle of $60^{\circ }$ |
| | with each other. Construct the vector that represents the resultant of the two forces. |
Using the vectors shown, construct:
| 4. | $2{\overrightarrow {AB}}+3{\overrightarrow {AB}}$ |
| 5. | ${\overrightarrow {AB}}+{\overrightarrow {CD}}$ |
| 6. | $2({\overrightarrow {AB}}+{\overrightarrow {CD}})$ |
| 7. | ${\overrightarrow {AB}}+{\overrightarrow {CD}}+{\overrightarrow {EF}}$ |
| 8. | ${\overrightarrow {AB}}+{\overrightarrow {CD}}+{\overrightarrow {EF}}+{\overrightarrow {GH}}$ |

## Subtracting Vectors

Using the vectors shown, construct:
| 1. | ${\overrightarrow {AB}}-{\overrightarrow {EF}}$ |
| 2. | $-{\overrightarrow {AB}}$ |
| 3. | $-3{\overrightarrow {GH}}$ |
| 4. | ${\overrightarrow {EF}}-{\overrightarrow {AB}}$ |
| 5. | $({\overrightarrow {AB}}+{\overrightarrow {CD}})-{\overrightarrow {EF}}$ |
Using parallelogram $ABCD$ with vectors as indicated, complete the following:
| 6. | ${\overrightarrow {AC}}-{\overrightarrow {AB}}=?$ |
| 7. | ${\overrightarrow {AC}}-{\overrightarrow {AD}}=?$ |
| 8. | ${\overrightarrow {AB}}=-?$ |