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Home  >>  CBSE XII  >>  Math  >>  Vector Algebra
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Choose the correct answer if θ is the angle between two vectors \( \overrightarrow a\) and \( \overrightarrow b\), then \( \overrightarrow a \: . \: \overrightarrow b\ \: \geq 0\) only when

\[ \begin{array} (A)\; 0 < \theta < \frac{\pi}{2} \quad & (B)\; 0 \: \leq\: \theta\: \leq \: \frac{\pi}{2} \quad \\(C)\; 0 < \theta < \pi \quad &(D)\; 0\: \leq\: \theta\: \leq \: \pi \end{array} \]

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  • $\overrightarrow a.\overrightarrow b=|\overrightarrow a||\overrightarrow b|\cos\theta$
  • If $\cos\theta>0$,then $\theta $ lies in the first quadrant.
Step 1:
Given $\overrightarrow a.\overrightarrow b\geq 0$
$\Rightarrow |\overrightarrow a||\overrightarrow b|\cos\theta\geq 0$
This implies $\cos\theta\geq 0$
Step 2:
We know $|\overrightarrow a|$ is positive and $|\overrightarrow a|$ is positive.
Therefore $\theta$ should lie in the first quadrant.
Therefore $0\leq \theta\leq \large\frac{\pi}{2}$
Hence the correct answer is B.
answered May 24, 2013 by sreemathi.v

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