Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Determine the octant(s)
in which  is located so that the condition(s) is (are)
satisfied.
a. | Octants I, II, III, IV (above the  -plane) | b. | Octant II (above
the  -plane) | c. | Octants I, II, III, IV (above the xy-plane) | d. | Octants II, IV, VI, VIII (above the xy-plane)
| e. | Octant IV (above the  -plane)
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2.
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Find the distance
between the points.
a. | 
units | b. | 
units | c. | 
units | d. | 
units | e. | 
units |
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3.
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Find the midpoint of
the line segment joining the points.
a. | ( ,  ,  ) | b. | ( ,
 ,  ) | c. | ( ,  ,  ) | d. | ( ,  ,   ) | e. | ( ,  ,  ) |
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4.
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Find the standard form
of the equation of the sphere with the given characteristics.
Center:  ;
radius: 
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5.
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Find the coordinates of the point located 6 units
behind the yz-plane, 4 units to the left of the xz-plane, and 8 units above the
xy-plane.
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6.
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Find the standard form of the equation of the
sphere with the given characteristics.
Center: (9, 8,
–9); radius 9
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7.
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Find the angle  between the
vectors. Round your answer to two decimal places.
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8.
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Find the angle  between the
vectors. Round your answer to two decimal places.
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9.
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Find the angle between the vectors u and
v. Express your answer in degrees and round to the nearest tenth of a degree.
u = –2i –3j –3k, v
= –2i –2j –7k
a. | 41.2° | b. | 61.1° | c. | 48.8° | d. | 28.9° | e. | 90° |
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10.
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The weight of a crate is 500 newtons. Find the
tension in each of the supporting cables shown in the figure. The coordinates of the points A,
B, C, and D are given below the figure. Round to the nearest
newton.
[Figure not necessarily to scale.]
point
A = (0,0,–110), point B = (100,0,0), point C =
(–50,50,0), point D = (0,–180,0)
a. | cable AB = 190; cable AC = 334; cable
AD = 150 | b. | cable AB =
334; cable AC = 190; cable AD = 150 | c. | cable AB = 190; cable AC = 150; cable AD =
334 | d. | cable AB = 150; cable AC = 334; cable
AD = 190 | e. | cable AB =
334; cable AC = 150; cable AD = 190 |
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11.
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Use the vectors u and v to find  .
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12.
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Find a unit vector orthogonal to u and
v.
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13.
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Find the area of the parallelogram that has the
vectors as adjacent sides.
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14.
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Find the area of the parallelogram that has the
vectors as adjacent sides.
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15.
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Find  and show that it is
orthogonal to both u and v.
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16.
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Find the area of the parallelogram that has the
vectors as adjacent sides.
u =  ,
v = 
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17.
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Find a set of symmetric equations of the line that
passes through the given points.
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18.
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Find a set of parametric equations of the line that
passes through the given points.
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19.
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Find the general form of the equation of the plane
passing through the point and perpendicular to the specified vector. [Be sure to reduce the
coefficients in your answer to lowest terms by dividing out any common factor.]
(8, 6, 3), n = i – 6j +
k
a. | x – 6y + z + 25 =
0 | b. | 8x + 6y + 3z – 25 =
0 | c. | x – 6y + z – 25 =
0 | d. | x – 6y + z =
0 | e. | 8x + 6y + 3z + 25 =
0 |
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20.
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Find the angle between the two planes.
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