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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
If $\vec p$ and $\vec q$ are unit vectors such that $\left[ {\vec p\,\vec q\,\vec p \times \vec q} \right] = \frac{1}{2}$ , then angle between $\vec p$ and $\vec q$ is
  • A
    $\frac{\pi }{6}$
  • ✓
    $\frac{\pi }{4}$
  • C
    ${\sin ^{ - 1}}\left( {\frac{1}{4}} \right)$
  • D
    $\frac{\pi }{2}$
✓

Answer

Correct option: B.
$\frac{\pi }{4}$
b
$(\overrightarrow p  \times \overrightarrow q ) \cdot (\overrightarrow p  \times \overrightarrow q ) = \frac{1}{2}$

$\Rightarrow \sin ^{2} \theta=\frac{1}{2} \Rightarrow \theta=\frac{\pi}{4}$

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