If \theta is the angle between vectors \vec{a} and \vec{b} such that \vec{a}\cdot\vec{b}\geq 0, then which one of the following is correct?

  1. A. 0\leq \theta \leq \pi
  2. B. \frac{\pi}{2}\leq \theta \leq \pi
  3. C. 0\leq \theta \leq \frac{\pi}{2} ✓
  4. D. 0\lt \theta \lt \frac{\pi}{2}

Correct Answer: C. 0\leq \theta \leq \frac{\pi}{2}

Explanation

We know that \vec{a}\cdot\vec{b} = |\vec{a}||\vec{b}|\cos\theta. If \vec{a}\cdot\vec{b} \geq 0, then \cos\theta \geq 0. The angle \theta between any two vectors is defined in the interval [0, \pi]. In this interval, \cos\theta \geq 0 restricts \theta to 0 \leq \theta \leq \frac{\pi}{2}.

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