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Mathematics · JEE | VECTOR ALGEBRA

हिन्दी

If \( \theta \) is the angle between two vectors \( \vec{a} \) and \( \vec{b} \), then \( \vec{a}\cdot\vec{b} \geq 0 \) only when:

  1. A
    \( 0 < \theta < \pi \)
  2. B
    \( 0 < \theta < \frac{\pi}{2} \)
  3. C
    \( 0 \leq \theta \leq \frac{\pi}{2} \)
  4. D
    \( 0 \leq \theta \leq \pi \)
View Answer & Solution

Correct answer · Option C

\( 0 \leq \theta \leq \frac{\pi}{2} \)

Explanation

Dot product \( \vec{a}\cdot\vec{b} = |\vec{a}||\vec{b}|\cos\theta \). For this to be greater than or equal to zero, \( \cos\theta \geq 0 \), which means \( 0 \leq \theta \leq \frac{\pi}{2} \).
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