Dot Product and Work — Unit test Answers

Vectors u and v have magnitudes of 20 and 13, respectively, and the angle between them is 210°. What is the scalar projection of u onto v?

Given vectors u = ⟨3, 4⟩ and v = ⟨4, 3⟩, what is the measure of the angle between the vectors?

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

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

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

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

Review the diagram.

Review the graph.

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

Given vectors u = ⟨–2, 1⟩ and v = ⟨4, –2⟩, which statement is true concerning u and v?

Two planes take off from the same airport at approximately the same time. Plane A has an airspeed of 600 mph and travels in the direction S 20° W. Plane B has an airspeed of 450 mph and travels in the direction N 35° E.Which diagram represents the distance, x, between the planes?

A vector in standard position has its terminal point at (7, –4). What is the magnitude of the vector?

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?

Review the graph.