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Chap2
1. Chapter 3, Concept Question 5
Which of the arrangements of axes in Fig. 3-23 can be labeled “right-handed coordinate system”? As usual, each axis
label indicates the positive side of the axis.
(a)
(b)
(c)
(d)
(e)
(f)
2. Chapter 3, Concept Question 9
If
and
is perpendicular to
, then what is the direction of
in the three situations shown in
Fig. 3-24?
(a) Situation (1), q positive:
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+x
+y
-x
-y
+z
-z
Situation (1), q negative:
+y
-z
-x
-y
+z
+x
Situation (2), q positive:
-x
-z
-y
+z
+x
+y
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Situation (2), q negative:
+x
-y
-x
+y
+z
-z
Situation (3), q positive:
-y
+y
+z
+x
-z
-x
Situation (3), q negative:
-z
+y
+z
+x
-y
-x
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3. *Chapter 3, Problem 1
What are (a) the x component and (b) the y component of a vector
in the xy plane if its direction is 213°
counterclockwise from the positive direction of the x axis and its magnitude is 6.6 m?
(a) Number
-5.535225748440
Units m
(b) Number
-3.594617631099
Units m
4. *Chapter 3, Problem 32
In figure, a vector a with a magnitude of 14.6 m is directed at angle θ = 70o counterclockwise from the +x axis. What
are the components (a)ax and (b)ay of the vector? A second coordinate system is inclined by angle θ' = 18o with respect
to the first. What are the components (c)a'x and (d)a'y in this primed coordinate system?
Fig. 3-31
Problem 32.
(a) Number
4.993494092555
(b) Number
13.719512263474
(c) Number
8.988657539755
(d) Number
11.504957002658
Units m
Units m
Units m
Units m
5. *Chapter 3, Problem 6
In Fig 3-27, a heavy piece of machinery is raised by sliding it a distance d = 15.5 m along a plank oriented at angle θ =
34.4° to the horizontal. (a) How high above its original position is it raised? (b) How far has it moved horizontally?
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Fig. 3-27
Problem 6.
(a) Number
8.756988553087
(b) Number
12.789259223314
Units m
Units m
6. *Chapter 3, Problem 28
Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.55 m due east, then 0.78 m at 34o north of
due east. Beetle 2 also makes two runs; the first is 1.72 m at 34o east of due north. What must be the magnitude of its
second run if it is to end up at the new location of beetle 1?
Number
1.017251957635
Units m
Significant digits are disabled; notolerance
7. *Chapter 3, Problem 36
If d1 = 5i - 2j + 10k and d2 = 4i - 8j + 8k, then what is (d1 + d2) · (d1 × 4d2)?
0
Significant digits not applicable; exact number, no tolerance
8. Reading Question 3.11
What is the direction of the result of the cross product of vectors
perpendicular to the plane of vectors
in the plane of vectors
and
?
and
and
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9. Test Bank, Question 7
The vector
in the diagram is equal to:
10. Test Bank, Question 12
Vectors
lie in the xy plane. We can deduce that
if:
A x + A y = Bx + B y
Ax = Bx and Ay = By
Ay/Ax = By/Bx
Ax2 + Ay2 = Bx2 + By2
Ax = Ay and Bx = By
11. Test Bank, Question 36
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The two vectors
and
define a plane (it is the plane of the
triangle with both tails at one vertex and each head at one of the other vertices). Which of the following vectors is
perpendicular to the plane?
12. Test Bank, Question 37
Let
and
90°, where
is the angle between
and
when they are drawn with their
tails at the same point. Which of the following is NOT true?
13. *Chapter 3, Problem 61
What are (a) the x component, (b) the y component, and (c) the z component of
4.1 ,
= -4.7 + 5.6 + 3.9 , and
(e) What is the component of
=
-
= 2.7 + 8.3 + 7.7 . (d) Calculate the angle between
along the direction of
+
if
= 3.0 + 2.2 -
and the positive z axis.
? (f) What is the magnitude of the component of
perpendicular
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to the direction of
(a)
but in the plane of
and
?
10.4
(b)
4.9
(c)
-0.3
(d) Number
91.494785563658
(e)
-2.144546800314
(f)
5.104010092199
Units ° (degrees)
14. *Chapter 3, Problem 63
Here are three vectors in meters:
d1 = -2.4i + 8.4j + 4.6k
d2 = -2.0i - 4.0j + 2.0k
d3 = 2.0i + 3.0j + 1.0k
What results from (a)d1 · (d2 + d3), (b)d1 · (d2 × d3), and d1 × (d2 + d3) ((c), (d) and (e) for i, j and k components
respectively)?
Give your answers in standard SI units.
(a) Number
5.4
(b) Number
83.6
Units m^2
Units m^3
(c) Number
29.8
Units m^2
(d) Number
7.2
Units m^2
(e) Number
2.4
Units m^2
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