8. Vectors

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

v - u

Point S lies between points R and T on a straight line. If $RT$ is $10$ centimeters long and $RS$ is $4$ centimeters, what is the length of $ST$?

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

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)

In Exercises 27–30, let v = i - 5j and w = -2i + 7j. Find each specified vector or scalar.

w - v

A force of 25 lb is required to hold an 80-lb crate on a hill. What angle does the hill make with the horizontal? 

Given vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $-2u ⃗+3v ⃗$.

Two forces of 128 lb and 253 lb act on a point. The resultant force is 320 lb. Find the angle between the forces.

CONCEPT PREVIEW 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.

-b

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.

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

|u| = 12, |v| = 20, θ = 27°

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

〈15, -8〉

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.

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

〈2, 0〉

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

θ = 50°, |v| = 26