MCQ
If $a, b, c$ be any three non-coplanar vectors, then $[a + b\,\,\,b + c\,\,\,c + a] = $
- A$|a\,b\,c|$
- ✓$2$$[a\,b\,c]$
- C${[\,a\,b\,c\,]^2}$
- D$2\,{[\,a\,b\,c\,]^2}$
$ = (a + b).(b \times c + b \times a + c \times c + c \times a)$
$ = (a + b).(b \times c + b \times a + c \times a)$, $\left\{ {\because \,c \times c = 0} \right\}$
$ = a.b \times c + a.b \times a + a.c \times a + b.b \times c$$ + b.b \times a + b.c \times a$
$ = [a\,b\,c] + [b\,c\,a] = 2[a\,b\,c]$.
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