Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve RD Sharma Class 12 Chapter 23 Scalar or Dot Product Exercise Very Short Answer Question 41 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 23 Scalar or Dot Product Exercise Very Short Answer Question 41 Maths Textbook Solution.

Answers (1)

best_answer

Answer:  \frac{2\pi}{3}

Given:  |\vec{a}|=|\vec{b}|=1 \text { and }|\vec{a}+\vec{b}|=1

Hint: Apply the identity  (a+b)^{2}

Solution:  |\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+|\vec{b}|^{2}+2 \cdot \vec{a} \cdot \vec{b}

\left[\because(a+b)^{2}=a^{2}+b^{2}+2 a b\right]

\Rightarrow(1)^{2}=(1)^{2}+(1)^{2}+2 \cdot \vec{a} \cdot \vec{b}

[\because|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}|=1,|\overrightarrow{\mathrm{a}}|=1 \&|\overrightarrow{\mathrm{b}}|=1]

\begin{aligned} &\Rightarrow 1=2+2 \vec{a} \cdot \vec{b} \\ & \end{aligned}

\Rightarrow-1=2 \vec{a} \cdot \vec{b} \\

\Rightarrow \vec{a} \cdot \vec{b}=\frac{-1}{2}

Now, we know   \operatorname{Cos} \theta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}

\begin{aligned} &\Rightarrow|\vec{a}||\vec{b}| \operatorname{Cos} \theta=\frac{-1}{2}\qquad\left[\because \vec{a} \cdot \vec{b}=\frac{-1}{2}\right] \\ & \end{aligned}

\Rightarrow \operatorname{Cos} \theta=\frac{-1}{2}\qquad[\because|\vec{a}|=|\vec{b}|=1] \\

\Rightarrow \theta=\frac{2 \pi}{3} \qquad\left[\because \operatorname{Cos} \frac{2 \pi}{3}=\frac{-1}{2}\right]

 

Posted by

infoexpert27

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

Centre, CBSE, NCERT defend NEP three-language policy in SC; seek dismissal of pleas against framework
anam-khan

Supreme Court to hear plea against CBSE evaluation policy for Gulf Class 12 students on July 14
anam-khan

'Award grace marks': CBSE's July 28 supplementary exam sparks student outrage over college admissions

Latest Question