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 42 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 23 Scalar or Dot Product Exercise Very Short Answer Question 42 Maths Textbook Solution.

Answers (1)

best_answer

Answer:  \frac{\pi}{6}

Given:  |\vec{a}|=|\vec{b}|=1 \text { and }(\sqrt{3} \vec{a}-\vec{b})=1

Hint: Apply the identity  (a-b)^{2}

Solution:   (\sqrt{3} \vec{a}-\vec{b})=1

\begin{aligned} &\Rightarrow(\sqrt{3} \vec{a}-\vec{b})^{2}=1^{2} \quad(\text { squaring both sides }) \\ & \end{aligned}  

\Rightarrow 3|\vec{a}|^{2}+|\vec{b}|^{2}-2(\sqrt{3} \vec{a}-\vec{b})=1

\begin{aligned} &{\left[\because(a-b)^{2}=a^{2}+b^{2}-2 a b\right]} \\ & \end{aligned}

\Rightarrow(3 \times 1)^{2}+(1)^{2}-2 \sqrt{3} \vec{a} \cdot \vec{b}=1 \quad[\because|\vec{a}|=|\vec{b}|=1]

\begin{aligned} &\Rightarrow \quad 3+1-2 \sqrt{3} \vec{a} \cdot \vec{b}=1 \\ & \end{aligned}

\Rightarrow-2 \sqrt{3} \vec{a} \cdot \vec{b}=-3 \\

\Rightarrow \quad \vec{a} \cdot \vec{b}=\frac{+3}{+2 \sqrt{3}} \\

\Rightarrow \vec{a} \cdot \vec{b}=\frac{\sqrt{3}}{2}

\begin{array}{ll} \Rightarrow|\vec{a}||\vec{b}| \operatorname{Cos} \theta=\frac{\sqrt{3}}{2} &\qquad {\left[\because \operatorname{Cos} \theta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}\right]} \\ \end{array}

\Rightarrow \operatorname{Cos} \theta=\operatorname{Cos} \frac{\pi}{6} \qquad\left[\because|\vec{a}|=|\vec{b}|=1 \& \operatorname{Cos} \frac{\pi}{6}=\frac{\sqrt{3}}{2}\right] \\

\Rightarrow \theta=\frac{\pi}{6}

 

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

CBSE explains 'roll number not found' error on portal amid student concerns
anam-khan

Congress attacks Dharmendra Pradhan over CBSE row, alleges failures in exam and revaluation process
anam-khan

CBSE retains Coempt for Class 12 revaluation amid OSM controversy, shifts data to its own servers: Reports

Latest Question