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.


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-b

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〉

Find the dot product for each pair of vectors.

〈6, -1〉, 〈2, 5〉

Find the dot product for each pair of vectors.

〈5, 2〉, 〈-4, -10〉

Find the dot product for each pair of vectors.

4i, 5i - 9j

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

〈5, 7〉

Given vectors u and v, find: 2u + 3v.

u = 2i, v = i + j