Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Find the coordinates of
the point.
The point is located on the  -axis, seven units in front
of the  -plane.
a. |  ,  ,
 | b. |  ,  , 
 | c. |  ,  ,   | d. |  ,  ,   | e. |  ,  ,   |
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2.
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Determine the octant(s)
in which  is located so that the condition(s) is (are)
satisfied.
a. | Octant II | b. | Octants II, IV, VI, VIII | c. | Octants I, II, III | d. | Octants I, II,
III, IV | e. | Octants III, IV, VII, or
VIII |
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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 center and
radius of the sphere.
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5.
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Find the magnitude of v.
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6.
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Find the magnitude of v.
Initial
point: 
Terminal point: 
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7.
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Find the dot product of u and
v.
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8.
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The vector v and its initial point are
given. Find the terminal point.
a. | Terminal point is  . | b. | Terminal point is
 . | c. | Terminal point is  . | d. | Terminal point is  . | e. | Terminal point is  . |
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9.
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The vector v and its initial point are
given. Find the terminal point.
a. | Terminal point is  . | b. | Terminal point is
 . | c. | Terminal point is  . | d. | Terminal point is  . | e. | Terminal point is  . |
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10.
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Find the dot product of u and
v.
u = –6i + 3j –
7k, v = –6i + 9j + 2k
a. | –12i + 12j –
5k | b. | 49 | c. | –5 | d. | 36i +
27j – 14k | e. | 77 |
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11.
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The vector v and its initial point are
given. Find the terminal point.
v = 
Initial point: (7, 4,
0)
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12.
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Use the triple scalar product to find the volume of
the parallelepiped having adjacent edges u,v,and w.
a. |  cubic
units | b. |  cubic
units | c. |  cubic
units | d. |  cubic
units | e. |  cubic
units |
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13.
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Use the vectors u and v to find  .
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14.
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Find the triple scalar product 
for the vectors
u =  ,
v =  , w = 
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15.
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Find the volume of the parallelepiped with the
given vertices.
A(6,–9,9), B(11,–8,5), C (12, –14, 4),
D (17, –13, 0), E (8, –5, 9),
F (13, –4, 5), G (14, –10,4),
H (19, –9, 0)
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16.
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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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17.
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Find the general form of the equation of the plane
passing through the point and perpendicular to the specified line. [Be sure to reduce the
coefficients in your answer to lowest terms by dividing out any common factor.]
a. | 3x – 8y + 4z + 39 =
0 | b. | 3x – 8y + 4z – 39 =
0 | c. | x – 3y + 3z – 39 =
0 | d. | x – 3y + 3z + 39 =
0 | e. | x – 3y + 3z =
0 |
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18.
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Find the general form of the equation of the plane
with the given characteristics.
The plane passes through the
point (–2, –3, –5) and is parallel to the yz-plane.
a. | x + y + z =
–10 | b. | y = –3 | c. | z = –5 | d. | y +
z = –8 | e. | x =
–2 |
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19.
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Determine whether the planes are parallel,
orthogonal, or neither.
5x – 2y –
4z = 6
–15x + 6y + 12z =
–16
a. | orthogonal | b. | parallel | c. | neither |
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20.
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Determine whether the planes are parallel,
orthogonal, or neither.
a. | Neither | b. | Parallel | c. | Orthogonal |
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