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 magnitude and
direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an
angle in [0,360°].
a. | 10 ;
225° | c. | 10 ;
45° | b. | 10; 225° | d. | 20; 45° |
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2.
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Find the magnitude and
direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an
angle in [0,360°].
a. | 9;
270° | c. | 3;
180° | b. | 3; 90° | d. | 3; 270° |
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3.
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Find the magnitude and
direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an
angle in [0,360°].
a. | 15;
157.4° | c. | 13;
112.6° | b. | 13; 22.6° | d. | 13; 157.4° |
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4.
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Find the magnitude and
direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an
angle in [0,360°].
a. | 6;
225° | c. | 12;
45° | b. | 6; 45° | d. | 6 ;
135° |
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5.
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Find the magnitude and
direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as an
angle in [0,360°].
a. | 14;
150° | c. | 14;
330° | b. | 28; 150° | d. | 28; 30° |
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6.
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Vector v has the given
magnitude and direction. Find the horizontal or vertical component of v, as indicated, if
è is the direction angle of v from the horizontal. Round to the
nearest tenth when necessary.
á = 46.7°,
|v| =
86.5; Find the horizontal component of v.
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7.
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Write the vector in the form
<a, b>. If necessary, round values to the nearest hundredth.
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8.
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Write the vector in the form
<a, b>. If necessary, round values to the nearest hundredth.
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9.
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Write the vector in the form
<a, b>. If necessary, round values to the nearest hundredth.
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10.
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Write the vector in the form
<a, b>. If necessary, round values to the nearest hundredth.
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11.
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Write the vector in the form
<a, b>. If necessary, round values to the nearest hundredth.
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12.
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Use the figure to find the
specified vector.
Find -a.
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13.
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Use the figure to find the
specified vector.
Find a
+ b.
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14.
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Find the indicated
vector.
Let u =
3i, v = i + j. Find 6u +
v.
a. | i + 19j | c. | 11i + j | b. | 19i +
j | d. | 19i +
6j |
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15.
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Find the indicated
vector.
Let u =  , v =  . Find u +
v.
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16.
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Find the indicated
vector.
Let u =  , v =  . Find v -
u.
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17.
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Find the indicated
vector.
Let u =  . Find 9u.
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18.
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Find the indicated
vector.
Let u =  . Find -9u.
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19.
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Find the component form of
the indicated vector.
Let
u =  , v =  . Find
u - v.
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20.
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Find the component form of
the indicated vector.
Let
u =  . Find 9u.
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21.
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Find the component form of
the indicated vector.
Let
u =  . Find -7u.
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22.
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Find the component form of
the indicated vector.
Let u =  , v =  .
Find -6u + v.
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23.
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Find the component form of
the indicated vector.
Let u =  , v =  .
Find -u - v.
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24.
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Write the vector in the form
ai + bj.
a. | -5i + 6j | c. | 5i + 6j | b. | 6i
+ 5j | d. | 6i -
5j |
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25.
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Find the dot product for the
pair of vectors.
 , 
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26.
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Find the dot product for the
pair of vectors.
 , 
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27.
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Find the dot product for the
pair of vectors.
5i
- 4j, 8i + j
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28.
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Find the dot product for the
pair of vectors.
-7j, 2i
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29.
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Find the angle between the
pair of vectors to the nearest tenth of a degree.  , 
a. | 152.7° | c. | 71.4° | b. | 142.7° | d. | 61.4° |
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30.
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Find the angle between the
pair of vectors to the nearest tenth of a degree. 5i - 4j, 2i -
6j
a. | 32.9° | c. | 33.9° | b. | 110.2° | d. | 60.4° |
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31.
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If u =  and v =  , evaluate (2u) · v.
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32.
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If u =  , v =  ,
and w =  , evaluate u · (v -
w).
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33.
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If u =  , v =  ,
and w =  , evaluate u · (v +
w).
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34.
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If u =  , v =  ,
and w =  , evaluate (u + v) ·
w.
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35.
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Determine whether the pair
of vectors is orthogonal.
 , 
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36.
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Determine whether the pair
of vectors is orthogonal.
 , 
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37.
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Determine whether the pair
of vectors is orthogonal.
 , 
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38.
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Determine whether the pair
of vectors is orthogonal.
 , 
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39.
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Determine whether the pair
of vectors is orthogonal.
3i - 8j, -8i + 3j
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