CHAPTER 3 Vectors (Pages 91-92)
66. To reach Moose Jaw, Canada, you drive your automobile due north 90 km, and then due west 70 km. What are the
magnitude and the direction of your displacement vector? What is the distance you traveled?
67. The displacement vector A has a length of350 m in the direction 45° west of north; the displacement vector B has a
length of 120 m in the direction 20° east of north. Find the magnitude and direction of the resultant of these
vectors.
68. In Chapter 10 we will become acquainted with the center of mass, which for a collection of equal particles is simply
the average position of the particles. Suppose that three particles have position vectors 5i + 3k, - 2i + j - 3k, and 4i +
2j + k, respectively. What is the average of these position vectors? What is the length of this average position
vector?
69. A vector drawn on a wall has a magnitude of2.0 and makes an angle of 30° with the vertical direction. What are the
vertical and horizontal components of this vector? ".
70. An aircraft flies 250 km in a direction 30° east of south, and then 250 km in a direction 30° west of south. What are
the magnitude and the direction of the resultant displacement vector?
71. The vector A has a length of 6.2 units in a direction 30° south of east. The vector B has a length of9.6 units in a
direction due south. What is the sum A + B of these vectors? What is the difference A - B?
72. A room measures 4 m in the x direction, 5 m in the y direction, and 3 ill in the z direction. A lizard crawls along the
walls from one corner of the room to the diametrically opposite comer. If the starting point is the origin of
coordinates, what is the displacement vector? What is the length of the displacement vector? If the lizard chooses
the shortest path along the walls, what is the length of its path?
73. What is the magnitude of the vector 2i + j - 4k?
74. Suppose that A = 4i - 2j and B = -3i - 4j. Calculate the following:
(a) A +B
(b) A-B
(e) 3A-B
75. The displacement vector A has a length of 50 m and direction of 30° east of north; the displacement vector B has a
length of 35 m and a direction 70° west of north. What is the dot product of these vectors?
76. The displacement vector A has a length of 6.0 m in the direction 30° east of north; the displacement vector B has a
length of 8.0 m in the direction 40° south of east. Find the magnitude and the direction of A X B.
77. Suppose that A = 3i + 4j and B = I + 3j – 2k. Find the component of B along the direction of A.
78. Given the vectors A = 2i + 2j – k and B = 3i – j, calculate
(a)
(b)
(c)
(d)
The sum A + B
The difference A - B
The dot product A ∙ B
The cross product A x B