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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
If $\vec a,\vec b,\vec c$ are non- zero and non-coplanar vectors such that $\left( {\vec a + \lambda \vec b} \right).\left[ {\left( {\vec b + 3\vec c} \right) \times \left( {\vec c - 4\vec a} \right)} \right] = 0$ , then $\lambda $ is equal to
  • A
    $0$
  • ✓
    $\frac {1}{12}$
  • C
    $\frac {7}{12}$
  • D
    $\frac {5}{12}$
✓

Answer

Correct option: B.
$\frac {1}{12}$
b
$[\vec a\,\vec b\,\vec c] \ne 0$

$ \Rightarrow \quad (1 - 12\lambda )[\vec a\,\vec b\,\vec c] = 0$

$\therefore \quad \lambda=\frac{1}{12}$

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