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

A force of 176 lb makes an angle of 78° 50′ with a second force. The resultant of the two forces makes an angle of 41° 10′ with the first force. Find the magnitudes of the second force and of the resultant.

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

-5v

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

Find the force required to keep a 3000-lb car parked on a hill that makes an angle of 15° with the horizontal.

To build the pyramids in Egypt, it is believed that giant causeways were constructed to transport the building materials to the site. One such causeway is said to have been 3000 ft long, with a slope of about 2.3°. How much force would be required to hold a 60-ton monolith on this causeway?

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

〈6, -3〉

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

〈2, 0〉