Unit Test — Unit test Answers

Let |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°. Which expression represents |r – s|?

Which diagram shows the parallelogram method for vector addition?

A vector has initial point at (3, –5) and terminal point at (–2, 3). What are the characteristics of this vector?

A force of 50 pounds acts in a direction 60° above horizontal, moving an object 100 feet from (0, 0) to (100, 0). How much work is done by the force?

Which equation represents a true sine ratio in ?

The magnitude of vector u is 34, and the magnitude of vector v is 20. The dot product u · v = –10. What is the approximate angle between the vectors?

Review the graph.

Two trains leave a station on different tracks. The tracks make an angle of 130°, with the station as a vertex. The first train travels 100 km and makes its first stop at point A, while the second train travels 200 km and makes it first stop at point B. How far apart are the trains when both are at their first stop? Round the answer to the nearest integer. [Not drawn to scale]

Review the diagram.

The speed of a boat in still water is 25 mph. The boat is traveling on a river with a current flowing south at 10 mph. At what angle upstream should the boat head to travel due west?

Review the graph.

Which equation below is equivalent to ?

Sameena measures the angle from the ground to the top of a building from two locations. The angle of elevation from the first point is 45°, and the angle of elevation from the second point is 60°. The distance from the second point to the top of the building is 150 ft. [Not drawn to scale]What is the distance from the first observation point to the top of the tower (x)? Round the answer to the nearest tenth.

Given u = ⟨2, –8⟩ and v = ⟨8, –2⟩, what is u · v?

Given vectors u = ⟨–2, 3⟩ and v = ⟨–6, 9⟩, what is the measure of the angle between u and v?

Let |u| = 4 at an angle of 210° and |v| = 9 at an angle of 315°, and w = u – v. What is the magnitude and direction angle of w?

A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling station along a path described by a vector with components . After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station.What are the characteristics of the vector representing the path of the ship?

Let u =. What is 3u?

A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction N 20° E. Which diagram represents the boat’s current distance, x, from the pier?

Let a = 2i + 9j, b = –4i + 5j, c = i – 3j, and d = 14j where i and j are unit vectors. What is (a – b) – (2d – c) in terms of i and j?