51. A sled is pulled along a level path through snow by a rope. A 30-lb force acting at an angle of 40° above the horizontal moves the sled 80 ft. Find the work done by the force.
51. A sled is pulled along a level path through snow by a rope. A 30-lb force acting at an angle of 40° above the horizontal moves the sled 80 ft. Find the work done by the force.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
Related questions
Question
51
Transcribed Image Text:17. a = (1, -4, 1), b = (0, 2, -2)
a=(-1,3, 4), b = (5, 2, 1)
19. a = 4i - 3j+ k, b = 2i - k
=8i-j+4k, b = 4j + 2k
18. a
20. a =
21-22 Find, correct to the nearest degree, the three angles of the
triangle with the given vertices.
21. P(2.0), Q(0, 3), R(3, 4)
22. A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)
23-24 Determine whether the given vectors are orthogonal,
parallel, or neither.
23. (a) a = (9, 3), b = (-2, 6)
(b) a = (4, 5, -2), b =(3,-1, 5)
(c) a = -8i + 12j + 4k, b = 6i - 9j - 3k
(d) a = 3i - j + 3k, b = 5i + 9j - 2k
24. (a) u = (-5, 4, -2),
v = (3, 4, -1)
(b) u = 9i - 6j + 3k,
(c) u = (c, c, c), v = (c, 0, -c)
v = -6i+4j - 2k
25. Use vectors to decide whether the triangle with vertices
P(1, -3, -2), Q(2, 0, -4), and R(6, -2, -5) is right-angled.
26. Find the values of x such that the angle between the vectors
(2, 1,-1), and (1, x, 0) is 45°.
27. Find a unit vector that is orthogonal to both i + j and i + k.
28. Find two unit vectors that make an angle of 60° with
= (3,4).
30. x + 2y = 7,
29-30 Find the acute angle between the lines.
29. 2x - y = 3,
3x + y = 7
=
20
5x - y = 2
31-32 Find the acute angles between the curves at their points of
intersection. (The angle between two curves is the angle between
their tangent lines at the point of intersection.)
31. y = x², y = x³
32. y sin x, y = cos x, 0≤x≤ π/2
33-37 Find the direction cosines and direction angles of the vector.
(Give the direction angles correct to the nearest degree.)
33. (2, 1, 2)
34. (6,3, -2)
35. i - 2j - 3k
36. i + j + k
37. (c, c, c), where c> 0
SECTION 12.3 The Dot Product
38. If a vector has direction angles a =
third direction angle y.
-
39-44 Find the scalar and vector projections of b onto a.
39. a = (-5, 12), b = (4, 6)
40. a = (1,4), b = (2,3)
41. a
b =
(3,-1, 1)
= (4,7,-4),
42. a = (-1, 4, 8), b = (12, 1, 2)
43. a = 3i 3j+ k,
44. a = i + 2j + 3k, b = 5i - k
TT/4 and 3 = π/3, find the
b = 2i + 4j - k
45. Show that the vector orth, b = b - projab is orthogonal to a.
(It is called an orthogonal projection of b.)
813
46. For the vectors in Exercise 40, find orth, b and illustrate by
drawing the vectors a, b, proja b, and orth, b.
47. If a =(3, 0, -1), find a vector b such that compab = 2.
48. Suppose that a and b are nonzero vectors.
(a) Under what circumstances is
compab comp, a?
(b) Under what circumstances is proja b = projь a?
=
49. Find the work done by a force F = 8i - 6j +9k that moves
an object from the point (0, 10, 8) to the point (6, 12, 20) along
a straight line. The distance is measured in meters and the force
in newtons.
50. A tow truck drags a stalled car along a road. The chain makes
an angle of 30° with the road and the tension in the chain is
1500 N. How much work is done by the truck in pulling the
qed car 1 km?
02
51. A sled is pulled along a level path through snow by a rope.
A 30-lb force acting at an angle of 40° above the horizontal
moves the sled 80 ft. Find the work done by the force.
52. A boat sails south with the help of a wind blowing in the direc-
tion S36°E with magnitude 400 lb. Find the work done by the
wind as the boat moves 120 ft.
|ax₁ + by₁ +c|
√a² + b²
53. Use a scalar projection to show that the distance from a point
P₁(x₁, y₁) to the line ax + by + c = 0 is
Use this formula to find the distance from the point (-2, 3) to
the line 3x - 4y + 5 = 0.
.
54. If r = (x, y, z), a = (a₁, a2, a3), and b = (b₁,b2, b3), show
that the vector equation (ra) (r - b) = 0 represents a
sphere, and find its center and radius.
55. Find the angle between a diagonal of a cube and one of its
edges.
Expert Solution
Step 1
Force:-
Force is defined as push or pull of an object having mass which causes change in it's velocity.
Unit of Force is N.
Here m is mass of object and a is acceleration.
Step by step
Solved in 3 steps with 3 images
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