Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Vector Algebra
0 votes

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

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

Can you answer this question?

1 Answer

0 votes
  • $\overrightarrow a.\overrightarrow b=|\overrightarrow a||\overrightarrow b|\cos\theta$
  • 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

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App