Given vectors u and v, find: 2u.

u = 2i, v = i + j

Given vectors u and v, find: 2u + 3v.

u = 2i, v = i + j

Given vectors u and v, find: v - 3u. 

u = 2i, v = i + j

Given vectors u and v, find: 2u. 

u = 〈-1, 2〉, v = 〈3, 0〉

Given vectors u and v, find: 2u + 3v. 

u = 〈-1, 2〉, v = 〈3, 0〉

Given vectors u and v, find: v - 3u. 

u = 〈-1, 2〉, v = 〈3, 0〉

Write each vector in the form a i + b j.

〈6, -3〉

Write each vector in the form a i + b j.

〈2, 0〉

Find the dot product for each pair of vectors.

4i, 5i - 9j

Find the angle between each pair of vectors. Round to two decimal places as necessary.

〈2, 1〉, 〈-3, 1〉

Find the angle between each pair of vectors. Round to two decimal places as necessary.

〈4, 0〉, 〈2, 2〉

Find the angle between each pair of vectors. Round to two decimal places as necessary.

〈1, 6〉, 〈-1, 7〉

Find the angle between each pair of vectors. Round to two decimal places as necessary.

3i + 4j, j

Find the angle between each pair of vectors. Round to two decimal places as necessary.

2i + 2j, -5i - 5j

Let u = 〈-2, 1〉, v = 〈3, 4〉, and w = 〈-5, 12〉. Evaluate each expression.

(3u) • v

Let u = 〈-2, 1〉, v = 〈3, 4〉, and w = 〈-5, 12〉. Evaluate each expression.

u • v - u • w

Determine whether each pair of vectors is orthogonal.

〈1, 1〉, 〈1, -1〉

Determine whether each pair of vectors is orthogonal.

√5i - 2j, -5i + 2 √5j

Determine whether each pair of vectors is orthogonal.

i + 3√2j, 6i - √2j

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

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

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°

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.

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?

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.)