Let a, b,c be three vectors from , a (b c)=(a b) c if - Vidyadip

MCQ

Let $a, b,c $ be three vectors from , $a\times (b\times c)=(a\times b)\times c$ if

✓
$b\times (a\times c)=0$
B
$a(b\times c)=0$
C
$c \times a = a \times b$
D
$c\times b=b\times a$

✓

Answer

Correct option: A.

$b\times (a\times c)=0$

a
(a) $\because $ We have $a \times (b \times c) = (a \times b) \times c$

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

$ \Rightarrow - \,(a\,.\,b)\,c = - \,(b\,.\,c)\,a$$ \Rightarrow \,\,(b\,.\,c)\,a - (b\,.\,a)\,c = 0$

$ \Rightarrow \,\,b \times (a \times c) = 0.$

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