Let u = ⟨–2, 6⟩, v = ⟨3, 2⟩, and w = ⟨–1, 4⟩. What is the magnitude and direction angle of 2(u + v) – 3w? 2.8; θ = 45.0°
6.4; θ = 38.7°
28.0; θ = 92.0°
41.0; θ = 51.3°

u = ⟨-2, 6⟩

v = ⟨3, 2⟩

w = ⟨-1, 4⟩

u + v = ⟨-2, 6⟩ + ⟨3, 2⟩

u + v = ⟨-2 + 3, 6 + 2⟩

u + v = ⟨1, 8⟩

2 (u + v) = 2 ⟨-1, 8⟩

2 (u + v) = ⟨2 • 1, 2 • 8⟩

2 (u + v) = ⟨2, 16⟩

-3 w = -3 ⟨-1, 4⟩

-3 w = ⟨-3 • (-1), -3 • 4⟩

-3 w = ⟨3, -12⟩

2 (u + v) - 3 w = 2 (u + v) + (-3 w)

2 (u + v) - 3 w = ⟨2, 16⟩ + ⟨3, -12⟩

2 (u + v) - 3 w = ⟨2 + 3, 16 + (-12)⟩

2 (u + v) - 3 w = ⟨5, 4⟩

Then the magnitude of this vector is

||2 (u + v) - 3 w|| = √(5² + 4²) = √41 ≈ 6.403

so the second choice is correct.

not enough information

step-by-step explanation:

we cannot know this, because the other students could have handed out 10 flyers, or they could have handed out 100. one way, the mean would go up, and another way, the mean would go down.