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1. |
Find the sum of  and  . |
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2. |
The magnitude of  is 41.3 meters and the magnitude of  is 53.6 meters. If and are perpendicular, what is the magnitude of their sum? |
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about 34.2 meters |
B. |
about 67.7 meters |
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C. |
about 54.0 meters |
D. |
about 41.9 meters |
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3. |
Let  . Find  . |
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4. |
Find the magnitude of the vector  . |
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5. |
Find  if  and  . |
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6. |
Write a vector equation describing a line passing through P1(2, 6) and parallel to  . |
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7. |
Write parametric equations of -2x + 5y = 9. |
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A. |
x = t and  |
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x = t and y = 9 - 5t |
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C. |
x = t and y = -2t + 5 |
D. |
x = -t and |
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8. |
Find the magnitude of the vector from the origin to point P(7, -5, 23). |
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5 |
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9. |
If  is the vector from the origin to point P(4, 5, 1), and  is the vector from the origin to point Q(-2, -9, 0), what is the ordered triple that represents  ? |
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10. |
Which pair of vectors is perpendicular? |
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11. |
In physics, you can determine how much force with which an object is sliding down a frictionless incline by adding the gravitational force vector and the ''normal force'' vector. The normal force vector is always directed up out of the incline perpendicular to it (90° more than the measure of the incline). The magnitude m of the normal force can be calculated by m = f cos  , where f is the gravitational force and is the angle measure of the incline. If a gravitational force (always straight down) of 50 N is being exerted on an object on a 25° incline, what is the magnitude of the force with which it is sliding down the incline? |
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A. |
21.1 N |
B. |
50 N |
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C. |
93.1 N |
D. |
45.3 N |
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12. |
If José pushes a cart horizontally, exerting a horizontal force of 0.5 N up a 45° incline so that the cart moves 3 m, how much work has José done on the cart? A joule (J) is the SI unit for work or energy. 1 J = 1 N · 1 m |
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A. |
 J |
B. |
 J |
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C. |
 J |
D. |
 J |
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13. |
Hetu is playing catch with a friend. If Hetu throws the ball at 21.3 m/s, at an angle of 30° with the horizontal, and his friend catches the ball at the same height from which Hetu threw it, how long is it before his friend catches the ball? |
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1.41 s |
B. |
0.46 s |
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C. |
10.65 s |
D. |
2.17 s |
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14. |
Hetu is playing catch with a friend. If Hetu throws the ball at 21.3 m/s, at an angle of 30° with the horizontal, and his friend catches the ball at the same height from which Hetu threw it, how far away is his friend standing? |
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23.1 m |
B. |
40.0 m |
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C. |
53.4 m |
D. |
46.2 m |
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15. |
Write a matrix that will translate a rectangular prism (which will always have 8 vertices) using the vector  . |
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16. |
Which of the following matrices represents a dilation by a scale factor of 2? |
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