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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
If $a,\,b,\,c$ are non-coplanar vectors and $d = \lambda a + \mu \,b + \nu c,$ then $\lambda $ is equal to
  • A
    $\frac{{[d\,b\,c]}}{{[b\,a\,c]}}$
  • ✓
    $\frac{{[b\,c\,d]}}{{[b\,c\,a]}}$
  • C
    $\frac{{[b\,d\,c]}}{{[a\,b\,c]}}$
  • D
    $\frac{{[c\,b\,d\,]}}{{[a\,b\,c]}}$
✓

Answer

Correct option: B.
$\frac{{[b\,c\,d]}}{{[b\,c\,a]}}$
b
(b) Since  $d=\lambda a+\mu b+\nu c$

$\therefore d.(b\times c)=\lambda \,a.(b\times c)+\mu \,b.(b\times c)+\mu \,c.(b\times c)$

$=\lambda \left[ abc \right]$

$⇒\lambda =\frac{[\,dbc]}{[abc]}$  $=\frac{[bcd]}{[bca]}$

 

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