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Scalar Or Dot Product — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsScalar Or Dot Product1 Mark
Question
If $\theta$ is the angle between two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ then $\vec{\text{a}}.\vec{\text{b}}\geq0$ only when:
  1. $0<\theta\frac{\pi}{2}$
  2. $0\leq\theta\leq\frac{\pi}{2}$
  3. $0<\theta<\pi$
  4. $0\leq\theta\leq\pi$
✓

Answer

  1. $0\leq\theta\leq\frac{\pi}{2}$

Solution:

$\vec{\text{a}}.\vec{\text{b}}\geq0$

$\Rightarrow|\vec{\text{a}}|\big|\vec{\text{b}}\big|\cos\theta\geq0$

$\Rightarrow\cos\theta\geq0$

$\Rightarrow0\leq\theta\leq\frac{\pi}{2}$

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