3
QuizMultiple Choice

Dot Product and Work — Unit test

Question 3 • Precalculus

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

Answer
A
The vectors form an obtuse angle of approximately 93°.
B
The vectors form an obtuse angle of approximately 96°.
C
The vectors form an obtuse angle of approximately 127°.
D
The vectors point in opposite directions.

Explanation

Since v = ⟨4, −2⟩ = −2⟨−2, 1⟩ = −2u, the vectors are scalar multiples with a negative scale factor. That means they point in opposite directions and form a 180° angle, not an obtuse angle near 90° or 127°. The true statement is that the vectors point in opposite directions.

AI-written and checked against the verified answer.

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