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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
Given vectors $a, b, c $ such that $a\,.(b \times c)$$ = \lambda \ne 0,\,$ the value of $(b \times c)\,.\,(a + b + c)/\lambda $ is
  • A
    $3$
  • ✓
    $1$
  • C
    $ - 3\lambda $
  • D
    $3/\lambda $
✓

Answer

Correct option: B.
$1$
b
(b) $\frac{(b\times c)\,.\,(a+b+c)}{\lambda }$   $=\frac{(b\times c)\,.\,a+(b\times c)\,.\,b+(b\times c)\,.\,c}{\lambda }$

$=\frac{(b\times c)\,.\,a+0+0}{\lambda }$
$ = \frac{\lambda }{\lambda } = 1$,

($\because $ Given $a.\,(b\times c)=\lambda =(b\times c)\,.\,a$)

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