8. Vectors

Starting at point A, a ship sails 18.5 km on a bearing of 189°, then turns and sails 47.8 km on a bearing of 317°. Find the distance of the ship from point A.

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

Given vectors u and v, find: v - 3u. 

u = 〈-1, 2〉, v = 〈3, 0〉

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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Given vectors $u ⃗$ and $v ⃗$, sketch the resultant vector $u ⃗+v ⃗$

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

Two parallel lines are crossed by a transversal. If one of the alternate interior angles is $y$ degrees and the corresponding angle on the other side of the transversal is $65$ degrees, what is the value of $y$?

Which statement is true about the relationship between points and planes in three-dimensional space?

Given that the vectors $u$, $v$, and $w$ satisfy $\left|u\right|=\left|v\right|=1$ and $u+v+w=0$, what is the magnitude of $w$?

In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar.

-4w

In the context of geometric vectors, what is the term for points that lie on the same plane?