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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
$(a + b)\,.\,(b + c) \times (a + b + c) = $
  • A
    $-[a b c]$
  • ✓
    $[a b c]$
  • C
    $0$
  • D
    $2[a b c]$
✓

Answer

Correct option: B.
$[a b c]$
b
(b) $(a + b)\,.\,(b + c) \times (a + b + c)$

$ = (a + b).\{ - \,a\, \times \,b\, + c \times a + b \times b + c \times b + b \times c + c \times c\} $

$ = (a + b)\,.\,\{ - \,a \times b + b \times c + c \times a + c \times b\} $

$[\because \,\,b \times b = 0\,o\,c \times c = 0]$

$ = (a + b).( - \,a \times b + c \times a)$

$ = - \,[a\,a\,b] + [a\,c\,a] - [b\,a\,b] + [b\,c\,a]$

$ = 0 + 0 - 0 + [b\,c\,a]$$ = [a\,b\,c]$.

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