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Encoding and Decoding Patterns

If a →×b → = ...

Question

$I f a^{\to} \times b^{\to} = c^{\to} a n d b^{\to} \times c^{\to} = a^{\to}, t h e n$

A

| b^{\to} | = | a^{\to} |

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B

| a^{\to} | = | c^{\to} |

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C

| c^{\to} | = | b^{\to} |

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D

none of these

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Solution

The correct option is B $| a^{\to} | = | c^{\to} |$
$\begin{matrix} G i v e n \to a \times \to b = \to c - - - (1) \to b \times \to c = \to a - - - (2) c a l c u l a t i n g (1) . \to c (\to a \times \to b) . \to c = \to c . \to c [\to a \to b \to c] = | \to c |^{2} A n d a l s o (2) . \to a \to a (\to b \times \to c) = \to a . \to a = | a |^{2} H e n c e, | a |^{2} = | \to c |^{2} \Rightarrow | \to a | = | \to c | O p t i o n B i s t h e c o r r e c t a n s w e r . \end{matrix}$

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