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 distance
between the points.
a. | 
units | b. | 
units | c. |  units | d. |  units | e. |  units |
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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 lengths of the
sides of the triangle with the indicated vertices.
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:  ;
diameter: 
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5.
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Find the vector z, given  .
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6.
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Find the vector z, given  .
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7.
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Find the magnitude of v.
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8.
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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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9.
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Determine whether u and v are
parallel, orthogonal, or neither.
u =  ,
v = 
a. | neither | b. | parallel | c. | orthogonal |
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10.
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Use the vectors u and v to find  .
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11.
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Find the area of the parallelogram that has the
vectors as adjacent sides.
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12.
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Find the area of the parallelogram that has the
vectors as adjacent sides.
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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 triple scalar product.
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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.
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17.
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Find a set of symmetric equations for the line
through the point and parallel to the specified vector or line.
Point: 
Parallel to: 
a. | Symmetric equations:  | b. | Symmetric
equations:  | c. | Symmetric equations:  | d. | Symmetric equations:  | e. | Symmetric equations:  |
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18.
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Find a set of symmetric equations of the line that
passes through the given points.
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19.
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Find a set of parametric equations of the
line.
Passes through  and is perpendicular to  .
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20.
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Find a set of parametric equations of the
line.
Passes through  and is parallel to  .
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