If a,b,c are vectors such that [abc ,]=4 , then [a b , ,b c , ,c … - Vidyadip

MCQ

If $a,b,c$ are vectors such that $[abc\,]=4$ , then $[a\times b\,\,b\times c\,\,c\times a]$ =

✓
$16$
B
$64$
C
$4$
D
$8$

✓

Answer

Correct option: A.

$16$

a
(a) $[a \times b\,\,b\, \times c\,\,c \times a] = (a \times b)\,.\,[(b \times c) \times (c \times a)]$

$ = (a \times b)\,.\,(\,[b\,c\,a]\,c - [b\,c\,c]\,a)$$ = (a \times b)\,.\,(\,[b\,c\,a]\,c - 0)$

$ = [b\,c\,a]\,[a\,b\,c] = [a\,b\,c]\,[a\,b\,c] = 4.4 = 16.$

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