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If \( \overrightarrow a.\overrightarrow a=0\: and \: \overrightarrow a.\overrightarrow b = 0\), then what can be concluded about the vector \( \overrightarrow b\)?

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  • $\overrightarrow a.\overrightarrow b=0$ if $\overrightarrow a$ is perpendicular to $\overrightarrow b$
  • $\overrightarrow a.\overrightarrow a=0$ if $\overrightarrow a=0$
$\overrightarrow a.\overrightarrow a=0$ and $\overrightarrow a.\overrightarrow b=0$
Then this implies if $\overrightarrow a=0$,then $\overrightarrow b$ is any vector.
Hence the conclusion is $\overrightarrow b$ is any vector.
answered Nov 11, 2013 by sreemathi.v
 

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