What is the angle between \( \vec{a} \) and \( \vec{b} \) ?
For the next two (02) items that follow : Let \( \vec{a}, \vec{b}, \vec{c}, \vec{a}+\vec{b}, \vec{b}+\vec{c}, \vec{a}+\vec{b}+\vec{c} \) be unit vectors.
- A. \frac{\pi}{6}
- B. \frac{\pi}{4}
- C. \frac{\pi}{2}
- D. \frac{2\pi}{3} ✓
Correct Answer: D. \frac{2\pi}{3}
Explanation
Since |a+b| = 1, we have |a|^2 + |b|^2 + 2|a||b|cos(\theta) = 1. This gives 1 + 1 + 2cos(\theta) = 1, meaning cos(\theta) = -1/2, so \theta = 2\pi/3.
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