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1. |
A quantity with only magnitude is called a _____. |
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A. |
matrix |
B. |
scalar |
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C. |
vector |
D. |
resultant |
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Hint |
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2. |
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 64 miles; about 77 miles |
B. |
about 87 miles; about 50 miles |
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C. |
about 50 miles; about 87 miles |
D. |
about 77 miles; about 84 miles |
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Hint |
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3. |
Write the ordered pair that represents 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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4. |
A vector that has a magnitude of one is called a _____. |
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A. |
scalar |
B. |
resultant |
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C. |
magnitude |
D. |
unit vector |
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Hint |
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5. |
Find the inner product of  and  if  and  . |
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A. |
14 |
B. |
-14 |
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C. |
-8 |
D. |
-12 |
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Hint |
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6. |
Find  if  and  . |
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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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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. |
24.2° |
B. |
12.6° |
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C. |
10.5° |
D. |
32.6° |
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Hint |
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8. |
Find the magnitude of the resultant vector for the diagram. |
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A. |
230.4 N |
B. |
250 N |
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C. |
237.2 N |
D. |
88 N |
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Hint |
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9. |
Suppose a football player kicks a football with an initial velocity of 22 yards per second at an angle of 63° to the horizontal. Suppose a kick returner catches the ball 3.6 seconds later. What is the vertical height of the ball at that time? |
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A. |
about 5.4 feet |
B. |
about 4.3 feet |
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C. |
about 2.6 feet |
D. |
about 3.9 feet |
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Hint |
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10. |
A football player kicks a football with an initial velocity of 25 yards per second at an angle of 77° to the horizontal. What is the hang time, the elapsed time between the moment the ball is kicked and the time it hits the ground? |
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A. |
about 4.4 seconds |
B. |
about 4.8 seconds |
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C. |
about 4.2 seconds |
D. |
about 4.6 seconds |
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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  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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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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13. |
Find the magnitude of  for N(-2, -6, -12) and K(3, -6, 7). |
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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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14. |
Write the parametric equations for the line passing through P(3, -4) and parallel to  . |
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A. |
x = t + 3 and y = 9t - 4 |
B. |
x = 3 + t and y = 4 – 9t |
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C. |
x = 3t + 1 and y = 4t - 9 |
D. |
x = 1 + 3t and y = 9 – 4t |
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Hint |
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15. |
Write parametric equations for y = 7x - 2. |
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A. |
x = 7t and y = -2 |
B. |
x = t and y = 7t - 2 |
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C. |
x = t and y =  |
D. |
x =  and y = -2 |
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Hint |
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16. |
Given the coordinates of a rectangular prism, represent them as a vertex matrix: A(1, 5, 3), B (1, 5, -1), C (1, -3, -1), D (1, -3, 3), E (-4, 5, 3), F (-4, 5, -1), G (-4, -3, -1), H (-4, -3, 3) |
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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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