8. Vectors

A force of 28.7 lb makes an angle of 42° 10′ with a second force. The resultant of the two forces makes an angle of 32° 40′ with the first force. Find the magnitudes of the second force and of the resultant.

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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.

Given vectors u and v, find: 2u. 

u = 〈-1, 2〉, v = 〈3, 0〉

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

〈5, 7〉

Determine if the following statement is true or false: Temperature is a vector. 

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

A crate is supported by two ropes. One rope makes an angle of 46° 20′ with the horizontal and has a tension of 89.6 lb on it. The other rope is horizontal. Find the weight of the crate and the tension in the horizontal rope.

A force of 18.0 lb is required to hold a 60.0-lb stump grinder on an incline. What angle does the incline make with the horizontal?

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

u • v - u • w

A force of 30.0 lb is required to hold an 80.0-lb pressure washer on an incline. What angle does the incline make with the horizontal?

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.

a + b

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.

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

Determine if the following statement is true or false: The vectors $v$ and $-v$ point in the same direction.