How to solve
cos θ shares its sign with u · v: positive means acute, zero means right, negative means obtuse.
Steps
- Compute the dot product.
- Positive → acute; zero → right; negative → obtuse.
- No magnitudes needed for the classification.
Example
u = (2, 1), v = (−1, 3). Angle type?
- u · v = −2 + 3 = 1 > 0.
- So the angle is acute.
Answer: acute
How to type answers
- Answer: acute, right, or obtuse
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