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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Vector Algebra

NDA 2023 · Mathematics · Vector Algebra

If θ is the angle between vectors a and b such that a · b ≥ 0 ,...

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

Options

  1. A0≤θ≤π0 \leq \theta \leq \pi
  2. Bπ2≤θ≤π\frac{\pi}{2} \leq \theta \leq \pi
  3. C0≤θ≤π20 \leq \theta \leq \frac{\pi}{2}
  4. D0<0<π20 < 0 < \frac{\pi}{2}

Correct answer

B. π2≤θ≤π\frac{\pi}{2} \leq \theta \leq \pi

Step-by-step solution

Since a⃗⋅b⃗≥0⇒∣a⃗∣∣b⃗∣cos⁡θ≥0⇒0→≤θ≤π2\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}
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