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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
If $|\vec{a}|=2,|\vec{b}|=5$ and $|\vec{a} \times \vec{b}|=8$, then $|\vec{a} \cdot \vec{b}|$ is equal to :
  • A
    $5$
  • B
    $4$
  • ✓
    $6$
  • D
    $3$
✓

Answer

Correct option: C.
$6$
c
$|\vec{a}|=2,|\vec{b}|=5$

$|\vec{a} \times \vec{b}|=|\vec{a}||\vec{b}| \sin \theta=\pm 8$

$\sin \theta=\pm \frac{4}{5}$

$\therefore \vec{a} \cdot \vec{b}=|\vec{a}| \vec{b} \mid \cos \theta$

$=10 \cdot\left(\pm \frac{3}{5}\right)=\pm 6$

$|\vec{a} \cdot \vec{b}|=6$

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