Vector Addition and Subtraction Answers

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

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

Review the following information about vectors q and r.q = ⟨–4, 1⟩r = ⟨a, 3⟩7(q + r) = ⟨–35, 28⟩

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

Let |q| = 5 at an angle of 45° and |r| = 16 at an angle of 300°. What is |q – r|?

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

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?

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⟩

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

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?

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

Vector u has initial point at (6, 8) and terminal point at (3, –2). Vector v has initial point at (–4, –3) and terminal point at (1, –7).What is u – v in component form?

Let |r| = 17 at an angle of 40° and |s| = 14 at an angle of 160°. Which expression represents |r + s|?

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