Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain Solution R.D.Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 46 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 46 Maths Textbook Solution.

Answers (1)

Answer:  xt\left ( -3,-2 \right )\: \: U\left ( 2,3 \right )

Hints: You must know the rules of solving vectors.

Given: \begin{aligned} &\vec{a}=x^{2} \hat{\imath}+2 \hat{\jmath}-2 \hat{k} \\ \end{aligned},\begin{aligned} &\vec{b}=\hat{\imath}-\hat{\jmath}+\hat{k} \\ \end{aligned},\begin{aligned} &\vec{c}=x^{2} \hat{\imath}+5 \hat{\jmath}-4 \hat{k} \end{aligned}

Solution: We have,

\begin{aligned} &\vec{a}=x^{2} \hat{\imath}+2 \hat{\jmath}-2 \hat{k} \\ &\vec{b}=\hat{\imath}-\hat{\jmath}+\hat{k} \\ &\vec{c}=x^{2} \hat{\imath}+5 \hat{\jmath}-4 \hat{k} \end{aligned}

Let \theta _{1} be the angle between \vec{a}and \vec{b}

      \theta _{2}      be the angle between \vec{b} and \vec{c}

Given that \theta _{1} is acute and  \theta _{2} is obtuse

\begin{aligned} &\Rightarrow \cos \theta_{1}>0 \quad \text { and } \theta_{2}<0 \\ \end{aligned}

\begin{aligned} &\Rightarrow \frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}>0 \text { and } \frac{\vec{b} \cdot \vec{c}}{|\vec{b}||\cdot \vec{c}|}<0 \\ \end{aligned}

\begin{aligned} &\Rightarrow \frac{x^{2}-4}{\sqrt{x^{4}+4+4} \sqrt{1+1+1}}>0 \quad \text { and } \frac{x^{2}-9}{\sqrt{x^{4}+25+16} \sqrt{1+1+1}}<0 \\ \end{aligned}

\begin{aligned} &\Rightarrow x^{2}-4>0 \quad \text { and } x^{2}-9<0 \end{aligned}

\begin{aligned} &\Rightarrow x t(-\infty,-2) U(2, \infty) \text { and } x t(-3,3) \\ \end{aligned}

\begin{aligned} &\Rightarrow x t(-3,-2) U(2,3) \end{aligned}

Posted by

infoexpert21

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

When will CBSE Class 12 results 2025 be declared? Last two years' trends
anam-khan

CBSE Class 10, 12 board exams 2025 from April 7 to 11 for sports students
anam-khan

CBSE Class 12 history paper 2025 moderately difficult, tested students’ understanding

Latest Question