8. Vectors

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

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.

〈-4, 4√3〉

Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.

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a + (b + c)

Refer to vectors a through h below. Make a copy or a sketch of each vector, and then draw a sketch to represent each of the following. For example, find a + e by placing a and e so that their initial points coincide. Then use the parallelogram rule to find the resultant, as shown in the figure on the right.

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c + d

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

For each pair of vectors u and v with angle θ between them, sketch the resultant.

|u| = 12, |v| = 20, θ = 27°

For each pair of vectors u and v with angle θ between them, sketch the resultant.

|u| = 20, |v| = 30, θ = 30°

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 parallelogram rule to find the magnitude of the resultant force for the two forces shown in each figure. Round answers to the nearest tenth.

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Two tugboats are pulling a disabled speedboat into port with forces of 1240 lb and 1480 lb. The angle between these forces is 28.2°. Find the direction and magnitude of the equilibrant.

Two rescue vessels are pulling a broken-down motorboat toward a boathouse with forces of 840 lb and 960 lb. The angle between these forces is 24.5°. Find the direction and magnitude of the equilibrant.

Two forces of 692 newtons and 423 newtons act on a point. The resultant force is 786 newtons. Find the angle between the forces.

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

v - u