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.

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.

Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.

〈5, 7〉

Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.

〈-4, -7〉

Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.

〈15, -8〉

Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary. See Example 1.

〈-7, 24〉

Find the magnitude and direction angle for each vector. Round angle measures to the nearest tenth, as necessary.

〈-4, 4√3〉

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〉

Vector v has the given direction angle and magnitude. Find the horizontal and vertical components.

θ = 50°, |v| = 26

Vector v has the given direction angle and magnitude. Find the horizontal and vertical components.

θ = 27° 30' |v| = 15.4

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

Write each vector in the form 〈a, b〉. Write answers using exact values or to four decimal places, as appropriate.

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Use the figure to find each vector: u + v. Use vector notation as in Example 4.

Use the figure to find each vector: u - v. Use vector notation as in Example 4.

Use the figure to find each vector: - u. Use vector notation as in Example 4.

Use the figure to find each vector: u + v. Use vector notation as in Example 4.

Use the figure to find each vector: u - v. Use vector notation as in Example 4.

Use the figure to find each vector: - u. Use vector notation as in Example 4.

Use the figure to find each vector: u + v. Use vector notation as in Example 4.

Use the figure to find each vector: u - v. Use vector notation as in Example 4.

Use the figure to find each vector: - v. Use vector notation as in Example 4.

Use the figure to find each vector: u + v. Use vector notation as in Example 4.

Use the figure to find each vector: u - v. Use vector notation as in Example 4.

Use the figure to find each vector: - u. Use vector notation as in Example 4.

Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.

v - u

Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.

-5v

Given u = 〈-2, 5〉 and v = 〈4, 3〉, find each of the following.

- 2u + 4v