Back
Problem 41a
Given vectors u and v, find: 2u.
u = 2i, v = i + j
Problem 41b
Given vectors u and v, find: 2u + 3v.
u = 2i, v = i + j
Problem 41c
Given vectors u and v, find: v - 3u.
u = 2i, v = i + j
Problem 43a
Given vectors u and v, find: 2u.
u = 〈-1, 2〉, v = 〈3, 0〉
Problem 43b
Given vectors u and v, find: 2u + 3v.
u = 〈-1, 2〉, v = 〈3, 0〉
Problem 43c
Given vectors u and v, find: v - 3u.
u = 〈-1, 2〉, v = 〈3, 0〉
Problem 46
Write each vector in the form a i + b j.
〈6, -3〉
Problem 47
Write each vector in the form a i + b j.
〈2, 0〉
Problem 53
Find the dot product for each pair of vectors.
4i, 5i - 9j
Problem 55
Find the angle between each pair of vectors. Round to two decimal places as necessary.
〈2, 1〉, 〈-3, 1〉
Problem 58
Find the angle between each pair of vectors. Round to two decimal places as necessary.
〈4, 0〉, 〈2, 2〉
Problem 61
Find the angle between each pair of vectors. Round to two decimal places as necessary.
〈1, 6〉, 〈-1, 7〉
Problem 63
Find the angle between each pair of vectors. Round to two decimal places as necessary.
3i + 4j, j
Problem 65
Find the angle between each pair of vectors. Round to two decimal places as necessary.
2i + 2j, -5i - 5j
Problem 67
Let u = 〈-2, 1〉, v = 〈3, 4〉, and w = 〈-5, 12〉. Evaluate each expression.
(3u) • v
Problem 69
Let u = 〈-2, 1〉, v = 〈3, 4〉, and w = 〈-5, 12〉. Evaluate each expression.
u • v - u • w
Problem 72
Determine whether each pair of vectors is orthogonal.
〈1, 1〉, 〈1, -1〉
Problem 75
Determine whether each pair of vectors is orthogonal.
√5i - 2j, -5i + 2 √5j
Problem 78
Determine whether each pair of vectors is orthogonal.
i + 3√2j, 6i - √2j
Problem 1
Use the law of sines to find the indicated part of each triangle ABC.
Find b if C = 74.2°, c = 96.3 m, B = 39.5
Problem 3
Use the law of sines to find the indicated part of each triangle ABC.
Find B if C = 51.3°, c = 68.3 m, b = 58.2 m
Problem 4
Use the law of sines to find the indicated part of each triangle ABC.
Find b if a = 165 m, A = 100.2°, B = 25.0°
Problem 48
One boat pulls a barge with a force of 100 newtons. Another boat pulls the barge at an angle of 45° to the first force, with a force of 200 newtons. Find the resultant force acting on the barge, to the nearest unit, and the angle between the resultant and the first boat, to the nearest tenth.
Problem 49
A plane has an airspeed of 520 mph. The pilot wishes to fly on a bearing of 310°. A wind of 37 mph is blowing from a bearing of 212°. In what direction should the pilot fly, and what will be her ground speed?
Problem 51
Find the force required to keep a 75-lb sled from sliding down an incline that makes an angle of 27° with the horizontal. (Assume there is no friction.)