If a, b, c be any three non-coplanar vectors, then [a + b , , ,b … - Vidyadip

MCQ

If $a, b, c$ be any three non-coplanar vectors, then $[a + b\,\,\,b + c\,\,\,c + a] = $

A
$|a\,b\,c|$
✓
$2$$[a\,b\,c]$
C
${[\,a\,b\,c\,]^2}$
D
$2\,{[\,a\,b\,c\,]^2}$

✓

Answer

Correct option: B.

$2$$[a\,b\,c]$

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

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

$ = (a + b).(b \times c + b \times a + c \times a)$, $\left\{ {\because \,c \times c = 0} \right\}$

$ = a.b \times c + a.b \times a + a.c \times a + b.b \times c$$ + b.b \times a + b.c \times a$

$ = [a\,b\,c] + [b\,c\,a] = 2[a\,b\,c]$.

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