a (b c)+b (c a)+c (a b)= - Vidyadip

MCQ

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

✓
$0$
B
$2[a b c]$
C
$a + b + c$
D
$3[a b c]$

✓

Answer

Correct option: A.

$0$

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

$\therefore a \times (b \times c) + b \times (c \times a) + c \times (a \times b)$

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

$=0$,

{$\because a.b = b.a$ etc.}

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