Trigonometry/Collection of Problems/Vectors
Identifying Vectors
editWhich 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 , , , draw the following:
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Given the rectangle , study the directions of the vectors, then indicate which statements are true and which are false:
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17. Using these two triangles we are given |
and |
Show that |
18. | Planes A, B, and C leave airport O at 8 A.M., plane A traveling N 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
edit1. | 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 |
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 |
with each other. Construct the vector that represents the resultant of the two forces. | |
Using the vectors shown, construct:
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Subtracting Vectors
editUsing the vectors shown, construct:
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Using parallelogram with vectors as indicated, complete the following:
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