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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
If $\vec a = 2\hat i + \hat j + \hat k,\vec b = \hat i + 2\vec j + 2\vec k,\vec c = \vec i + \vec j + 2\hat k$ and $\left( {1 + \alpha } \right)\hat i + \beta \left( {1 + \alpha } \right)\hat j + \gamma \left( {1 + \alpha } \right)\left( {1 + \beta } \right)\hat k = \hat a \times \left( {\vec b \times \vec c} \right)$ ,  then $\alpha ,\beta ,\gamma $ are
  • ✓
    $ - 2, - 4, - \frac{2}{3}$
  • B
    $  2, - 4,  \frac{2}{3}$
  • C
    $ - 2,  4,  \frac{2}{3}$
  • D
    $  2,  4, - \frac{2}{3}$
✓

Answer

Correct option: A.
$ - 2, - 4, - \frac{2}{3}$
a
$\vec{a} \times(\vec{b} \times \vec{c})=(\vec{a} \cdot \vec{c}) \vec{b}-(\vec{a} \cdot \vec{b}) \vec{c}$

$\Rightarrow \alpha=-2 ; \beta=-4: \gamma=-\frac{2}{3}$

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