Performing Operations with Complex Numbers — Unit test Answers

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

When deriving the Law of Cosines, the equation is created using the Pythagorean theorem. Use substitution to replace in the equation below and then simplify.

Solve the Law of Cosine: for cos C.

Which pair of equations below is a result of constructing the altitude, h, in ?

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

Which equation could be used to solve for the measure of side q in shown below, given s = 15, S = 45°, and Q = 105°? [Not drawn to scale]

Review the diagram.

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

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?

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?

Review the graph.

Review the graph.

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

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?

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

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

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

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 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?