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1. |
A ship leaving port sails for 100 miles in a direction 40° north of due east. Find the magnitude of the vertical and horizontal components. |
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A. |
about 87 miles; about 50 miles |
B. |
about 77 miles; about 84 miles |
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C. |
about 64 miles; about 77 miles |
D. |
about 50 miles; about 87 miles |
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Hint |
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2. |
Find the magnitude of the vector from X(-4, 7) to Y(3, -4). |
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A. |
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B. |
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C. |
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D. |
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Hint |
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3. |
Find the magnitude of the vector  . |
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A. |
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B. |
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C. |
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D. |
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Hint |
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4. |
Write  as the sum of unit vectors for A(4, 8, -6) and B(-2, 5, 0). |
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A. |
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B. |
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C. |
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D. |
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Hint |
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5. |
Find the magnitude of  for T(4, 0, -6) and M(5, -1, 0). |
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A. |
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B. |
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C. |
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D. |
6 |
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Hint |
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6. |
Find the inner product of  and  if  and  . |
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A. |
-12 |
B. |
-14 |
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C. |
-8 |
D. |
14 |
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Hint |
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7. |
Find the direction of the resultant of a 100-newton force along the x-axis and a 150-newton force at an angle of 40° above the x-axis. |
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A. |
12.6° |
B. |
24.2° |
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C. |
32.6° |
D. |
10.5° |
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Hint |
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8. |
Write a vector equation describing a line passing through P1(2, 6) and parallel to  . |
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A. |
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B. |
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C. |
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D. |
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Hint |
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9. |
Write parametric equations of y = -2x + 5. |
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A. |
x = -2t + 5 and y = t |
B. |
x = t and y = 2x - 5 |
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C. |
x = t and y = -2t + 5 |
D. |
x = t and y = 2t - 5 |
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Hint |
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10. |
Given the coordinates of the vertices of a triangular prism, represent them as a vertex matrix.
A(1, 2, -3) B(0, 1, -3) C(-1, 4, -3)
D(-1, 4, 5) E(1, 2, 5) F(0, 1, 5) |
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A. |
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B. |
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C. |
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D. |
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Hint |
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11. |
A transformation in three-dimensional space is represented by  . Which matrix represents this transformation? |
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A. |
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B. |
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C. |
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D. |
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Hint |
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12. |
If both the initial and terminal points of a vector are at the origin, the vector is __________. |
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A. |
the zero vector |
B. |
negative |
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C. |
linearly independent |
D. |
positive |
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Hint |
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13. |
Evaluate  if  and  . |
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A. |
44 |
B. |
21 |
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C. |
-39 |
D. |
60 |
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Hint |
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14. |
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 ˇ 1 m |
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A. |
 J |
B. |
 J |
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C. |
 J |
D. |
 J |
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Hint |
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15. |
Karla is in a contest to see who can hit a baseball the farthest. If she hits a ball with an initial velocity of 94.5 ft/s at an angle of 42° with the horizontal, how far will the ball travel before it hits the ground? |
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A. |
250 ft |
B. |
139 ft |
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C. |
395 ft |
D. |
277 ft |
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Hint |
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16. |
If a quarterback throws a 30-yard pass to his receiver with an initial velocity of 21 yards per second at an angle of 15 with the horizontal, how long is the ball in the air? |
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A. |
0.68 s |
B. |
1.48 s |
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C. |
1.43 s |
D. |
5.52 s |
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Hint |
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