If a×(b×c)=(a×b)×c then which of the following is incorrect ?

(a·c) b-(a·b) c=(c·a) b-(c·b) a ⇒ c=c·ba·b a ⇒ c || a ⇒ c ×a=0

If a×(b×c)=(a×b)×c then which of the following is incorrect ?

(a·c) b-(a·b) c=(c·a) b-(c·b) a ⇒ c=c·ba·b a ⇒ c || a ⇒ c ×a=0

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If $a \times (b \times c) = (a \times b) \times c$ then which of the following is incorrect ?

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$c \times a = 0$

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

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

$c . a = 0$

answer is A.

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Detailed Solution

$\begin{array}{rcl} (a \cdot c) b - (a \cdot b) c & = & (c \cdot a) b - (c \cdot b) a \\ \Rightarrow & c = \frac{c \cdot b}{a \cdot b} a \\ \Rightarrow & c | | a \Rightarrow c \times a = 0 \end{array}$

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