Dot Product and Work — Unit test Answers

Jake and Maddie each take the closest path from their homes to the store. Based on the picture below, what is the approximate difference in the distance each person traveled to the store?

Let q = ⟨15, –3⟩, r = ⟨–5, 8⟩, and s = ⟨10, –1⟩. What is r – q + 2s?

Let v = ⟨–13, 2⟩ and w = ⟨–9, –5⟩. What is w – v?

The bottom of a 12-foot ladder is placed on the ground 7 feet from the base of a pipe sticking out of the ground. The top of the ladder is placed an unknown distance off the ground, leaning on the pipe. The ladder and the ground meet at a 56.4° angle. At what angle does the pipe meet the ground?

What is the area of triangle ABC? Round to the nearest square unit.

A plane flies 35 km in the direction N 30° W, then flies 60 km in the direction N 60° E. How far is the plane from its original location?

Let u = ⟨1, 5⟩, v = ⟨–3, 3⟩, and w = ⟨2, 3⟩. What is the direction angle of 4w – (2u + v)?

Air traffic controllers are watching two planes on radar to ensure there is enough distance between them. Plane A took off at 10:00 a.m., and plane B took off at the same runway 5 minutes later. Both planes are flying at the same direction angle and the same path. At 10:10 a.m., the airport’s radar system detected plane A at (24, 18) and plane B at (8, 6). The scale on the radar is 1 unit = 25 miles.Which vector represents the path from plane A to plane B, and what is the actual distance between them?

From where Kiana is standing, she must look up at a 50° angle to see the top of a building. If she backs up 50 feet, she will need to look up at a 40° angle to see the top of the same building. Approximately how tall is the building?

Let a =⟨–7, 3⟩ and b =⟨–2, –12⟩, and c = a + b. What is the magnitude and direction angle of c?

A cyclist travels 5 miles in the direction N 30° E, then travels 3 miles in the direction N 70° E. Which equation measures the cyclist’s distance, x, from the starting point?

A tree is growing on a hill. In an attempt to make the tree grow straight up, a 12-foot-long wire is attached to a tree at a point 6 feet off the ground. The wire is anchored to the ground 10 feet from the base of the tree. At what angle is the tree growing in relation to the hill?

Based on the sketch below, how far is Joey’s house from the park?

Let w = where O(–5, 6) and R(4, –2). What is the component form of w?

Triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. What is the area of triangle RST? Round to the nearest square inch.Heron’s formula: Area