Q243 / 270 · NDA 2023 (Phase 2) · Mathematics

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?

  • A
    $0 \leq \theta \leq \pi$
  • Correct answer
    B
    $\frac{\pi}{2} \leq \theta \leq \pi$
  • C
    $0 \leq \theta \leq \frac{\pi}{2}$
  • D
    $0 \lt 0 \lt \frac{\pi}{2}$

Solution

Since $\vec{a} \cdot \vec{b} \geq 0 \Rightarrow|\vec{a}||\vec{b}| \cos \theta \geq 0 \Rightarrow \overrightarrow{0} \leq \theta \leq \frac{\pi}{2}$

Hence, the correct answer is option: 'B'.

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