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

$\begin{array}{1 1} (A) \overrightarrow b\; is \;collinear \;vector. \\ (B) \overrightarrow b\; is \;unit \;vector. \\ (C) \overrightarrow a\; and \;\overrightarrow b\;are \;equal\; vectors. \\ (D) \overrightarrow b is\; any\; vector. \end{array} $

1 Answer

  • $\overrightarrow a.\overrightarrow b=0$ if $\overrightarrow a$ is perpendicular to $\overrightarrow b$
  • $\overrightarrow a.\overrightarrow a=0$ if $\overrightarrow a=0$
Step 1:
$\overrightarrow a.\overrightarrow a=0$ and $\overrightarrow a.\overrightarrow b=0$
Then this implies if $\overrightarrow a=0$,then $\overrightarrow b$ is any vector.
Step 2:
Hence the conclusion is $\overrightarrow b$ is any vector.
answered May 21, 2013 by sreemathi.v

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