Vector Addition and Subtraction Quiz

Let u = ⟨-2, -3⟩ and v = ⟨3, -1⟩. Which graph shows u - v?

A.

Which graph shows u + v for the given vectors u and v?

A.

Let a = ⟨5, -9⟩ and b = ⟨-3, 1⟩, and c = b - a. What is the magnitude and direction angle of c?

A. |c| = 12.8; θ = 128.7°

Let u = ⟨-2, 6⟩, v = ⟨3, 2⟩, and w = ⟨-1, 4⟩. What is the magnitude and direction angle of 2(u + v) - 3w?

B. 6.4; θ = 38.7°

Let u = 2i + 3j, v = -i, and w = 5i - 6j. What is the magnitude of 2(u - v + w)?

C. 17.1

For the vectors u = ⟨2, 9⟩, v = ⟨4, -8⟩, and w = ⟨-12, 4⟩, what is u + v + w?

C. ⟨-6, 5⟩

Let a = 8i + 2j, b = -3i + j, and c = 2i - 5j, where i and j are unit vectors. What is 4a + 2b - 9c in terms of i and j?

D. 8i + 55j

Let |u| = 10 at an angle of 45° and |v| = 13 at an angle of 150°, and w = u + v. What is the magnitude and direction angle of w?

D. |w| = 14.2; θ = 107.1°

Let r = ⟨7, 1⟩, s = ⟨-6, 2⟩, and t = ⟨-9, -3⟩. What is 10r + s - t?

D. ⟨73, 15⟩

Let u = ⟨9, -2⟩, v = ⟨-4, 3⟩, and w = ⟨5, 1⟩. Kelcy incorrectly determined 3u - 5(v + w) to be ⟨32, -26⟩. Review her steps as shown. 3u - 5(v + w) 3⟨9, -2⟩ - 5[⟨-4, 3⟩ + ⟨5, 1⟩] ⟨27, -6⟩ - 5[⟨-1, 4⟩] ⟨27, -6⟩ + ⟨5, -20⟩ ⟨32, -26⟩ What mistake did Kelcy make?

What mistake did Kelcy make? A. She added ⟨-4, 3⟩ and ⟨5, 1⟩ incorrectly.