If a = 2 i + j + k, b = i + 2 j + 2 k, c = i + j + 2 k and ( 1 + ) i + ( 1 + ) j + ( 1 + ) ( 1 + ) k = a ( b c ) , then , , are

If a = 2 i + j + k, b = i + 2 j + 2 k, c = i + j + 2 k and ( 1 + …

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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