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Problem 56
A pilot is flying at 168 mph. She wants her flight path to be on a bearing of 57° 40′. A wind is blowing from the south at 27.1 mph. Find the bearing she should fly, and find the plane's ground speed.
Problem 58
A plane is headed due south with an airspeed of 192 mph. A wind from a direction of 78.0° is blowing at 23.0 mph. Find the ground speed and resulting bearing of the plane.
Problem 9
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.
〈5, 7〉
Problem 10
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.
〈-4, -7〉
Problem 11
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.
〈15, -8〉
Problem 12
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary. See Example 1.
〈-7, 24〉
Problem 13
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.
〈-4, 4√3〉
Problem 14
Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary. See Example 1.
〈8√2, -8√2〉
Problem 16
Vector v has the given direction angle and magnitude. Find the horizontal and vertical components.
θ = 50°, |v| = 26
Problem 18
Vector v has the given direction angle and magnitude. Find the horizontal and vertical components.
θ = 27° 30' |v| = 15.4
Problem 21
Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.
Problem 22
Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.
Problem 23
Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.
Problem 24
Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.
Problem 25
Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.
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Problem 27a
Use the figure to find each vector: u + v. Use vector notation as in Example 4.
Problem 27b
Use the figure to find each vector: u - v. Use vector notation as in Example 4.
Problem 27c
Use the figure to find each vector: - u. Use vector notation as in Example 4.
Problem 29a
Use the figure to find each vector: u + v. Use vector notation as in Example 4.
Problem 29b
Use the figure to find each vector: u - v. Use vector notation as in Example 4.
Problem 29c
Use the figure to find each vector: - u. Use vector notation as in Example 4.
Problem 30a
Use the figure to find each vector: u + v. Use vector notation as in Example 4.
Problem 30b
Use the figure to find each vector: u - v. Use vector notation as in Example 4.
Problem 30c
Use the figure to find each vector: - v. Use vector notation as in Example 4.
Problem 31a
Use the figure to find each vector: u + v. Use vector notation as in Example 4.
Problem 31b
Use the figure to find each vector: u - v. Use vector notation as in Example 4.
Problem 31c
Use the figure to find each vector: - u. Use vector notation as in Example 4.
Problem 34
Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.
v - u
Problem 36
Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.
-5v
Problem 38
Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.
- 2u + 4v
