Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors and $\theta $is the angle between them, then $(\overrightarrow{a}+\overrightarrow{b})$ is a unit vector if

\[\begin{array}{1 1}(1)\theta =\large\frac{\pi}{3}& (2)\theta =\large\frac{\pi}{4}\\ (3)\theta=\large\frac{\pi}{2}& (4)\theta=\large\frac{2\pi}{3}\end{array}\]

Can you answer this question?

1 Answer

0 votes
Given $|\overrightarrow{a}|=1$ and $|\overrightarrow{b}| =1$
$\theta$ is the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$
$\overrightarrow{a^2}+\overrightarrow{b^2}+2|\overrightarrow{a}||\overrightarrow{b}| \cos \theta=1$
$\overrightarrow{|a|^2}+\overrightarrow{|b|^2}+2|\overrightarrow{a}||\overrightarrow{b}| \cos \theta=1$
$1^2+1^2+2 \times 1\times 1 \cos \theta=1$
$\cos \theta = -\large\frac{1}{2}$
$\theta$ lies in the second quadrant
Hence 4 is the correct answer.
answered May 5, 2014 by meena.p

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