Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 29 maths

Explain solution RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 29 maths

Answers (1)

best_answer

Answer:

Option (a)  \frac{\pi }{6}

Hint:

You must know the identity (a-b)^{2}=a^{2}+b^{2}-2 a b

Given:

|\vec{a}|=|\vec{b}|=1 \text { and } \sqrt{3} \vec{a}-\vec{b} to be a unit vector

Solution:

\frac{\vec{a} \cdot \vec{b}}{|\vec{a}| \cdot|\vec{b}|}=\cos \theta                                                                            [\because|\vec{a}|=|\vec{b}|=1]

\vec{a} \cdot \vec{b}=\cos \theta                                                                                                                                              According to the given question,

\begin{aligned} &|\sqrt{3} \vec{a}-\vec{b}|=1 \Rightarrow|\sqrt{3} \vec{a}-\vec{b}|^{2}=1 \\\\ &3|\vec{a}|^{2}+|\vec{b}|^{2}-2 \sqrt{3}(\vec{a} \cdot \vec{b})=1 \\\\ &3+1-2 \sqrt{3} \cos \theta=1 \end{aligned}

\begin{aligned} &-2 \sqrt{3} \cos \theta=-3 \\\\ &2 \sqrt{3} \cos \theta=3 \\\\ &\cos \theta=\frac{3}{2 \sqrt{3}} \end{aligned}                    \left[\because \frac{\sqrt{3}}{2}=\cos \frac{\pi}{6}\right]

\begin{aligned} &\cos \theta=\frac{\sqrt{3}}{2} \\\\ &\theta=\frac{\pi}{6} \end{aligned}

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 10, 12 results 2024 likely after May 20, says result portal
anam-khan

CBSE Result Date 2024 Live: CBSE Class 10, 12 board results for 39 lakh students at cbse.nic.in after May 20
anam-khan

CBSE Results 2024: Last 9 years’ CBSE Class 10, 12 result date and time; links to check score

Latest Question