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1. |
Find the sum of  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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2. |
The magnitude of the zero vector is _____. |
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A. |
any negative number |
B. |
0 |
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C. |
any positive number except 1 |
D. |
1 |
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Hint |
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3. |
A vector that has a magnitude of one is called a _____. |
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A. |
resultant |
B. |
unit vector |
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C. |
magnitude |
D. |
scalar |
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Hint |
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4. |
Find an ordered triple to represent  in the equation  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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5. |
Find the parametric equations for a line parallel to  and passing through the point at (-3, -5). |
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A. |
x = 4 - 3t and y = -2 + 5t |
B. |
x = -4 + 3t and y = 2 + 5t |
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C. |
x = -4 - 3t and y = -2 - 5t |
D. |
x = -3 + 4t and y = -5 - 2t |
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Hint |
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6. |
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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7. |
Find the initial horizontal velocity and vertical velocity of a stone kicked with an initial velocity of 15 feet per second at an angle of 42° with the ground. |
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A. |
about 10 ft/s, about 22 ft/s |
B. |
about 11 ft/s, about 10 ft/s |
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C. |
about 14 ft/s, about 12 ft/s |
D. |
about 11 ft/s, about 13 ft/s |
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Hint |
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8. |
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. How far has the ball traveled horizontally? |
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A. |
about 108 feet |
B. |
about 154 feet |
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C. |
about 223 feet |
D. |
about 85 feet |
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Hint |
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9. |
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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10. |
A vector  that is represented by an ordered pair can ________ be written as the sum of unit vectors. |
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A. |
sometimes |
B. |
usually |
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C. |
never |
D. |
always |
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Hint |
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11. |
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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12. |
Two vectors  and  are perpendicular if ________. |
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A. |
their cross product equals zero |
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B. |
their inner product is v1w1 +v2w2 |
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C. |
their dot product is equal to their cross product |
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D. |
their inner product equals zero |
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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 · 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. |
Find the magnitude of the resultant of a 7-newton force at an angle of 35° above the x-axis and a 12-newton force at an angle of 35° below the x-axis. |
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A. |
7.4 N |
B. |
11.6 N |
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C. |
18.1 N |
D. |
15.8 N |
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Hint |
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16. |
Given what you know about matrix multiplication, make a conjecture about what kind of transformation in 3-dimensional space is represented by the matrix  . |
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A. |
The transformation is a reflection over the yz-plane, followed by a transformation over the xy-plane. |
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B. |
The transformation is a reflection over the xz-plane. |
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C. |
The transformation is a dilation by a scale factor of -1. |
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D. |
The transformation is a translation 1 unit along the y-axis. |
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Hint |
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