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⟩
Answer
A
She added ⟨–4, 3⟩ and ⟨5, 1⟩ incorrectly.
B
She did not correctly distribute 3 to both components of u.
C
She should have distributed –5 to both v and w before adding.
D
She should have subtracted ⟨27, –6⟩ and ⟨5, –20⟩, rather than adding.
Explanation
The vector addition is the first incorrect step: ⟨–4, 3⟩ + ⟨5, 1⟩ = ⟨1, 4⟩, not ⟨–1, 4⟩. So the error was adding the first components incorrectly. The other listed operations are consistent with her incorrect sum, making “She added ⟨–4, 3⟩ and ⟨5, 1⟩ incorrectly” the correct choice.
AI-written and checked against the verified answer.