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 Scaler and Dot Product exercise Multiple choice question 13 maths textbook solution

Please solve RD Sharma class 12 chapter 23 Scaler and Dot Product exercise Multiple choice question 13 maths textbook solution

Answers (1)

Answer:

Option (b)   0<x<\frac{1}{2}

Hint:

Use the formula of finding the angle between two vectors   \cos \theta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}

Given:

\vec{a}=2 x^{2} \hat{i}+4 x \hat{j}+\hat{k} \text { and } \vec{b}=7 \hat{i}-2 \hat{j}+x \hat{k}  angle between them is obtuse and angle between  \vec{b} and z-axis is acute and less than  \frac{\pi }{6}

Solution:

\vec{a}=2 x^{2} \hat{i}+4 x \hat{j}+\hat{k}, \vec{b}=7 \hat{i}-2 \hat{j}+x \hat{k}

Let \cos A be the angle between \vec{a} \text { and } \vec{b}

Since, A is obtuse angle

\begin{aligned} &\cos A<0 \\\\ &\frac{\vec{a} \cdot \vec{b}}{|\vec{a}||\vec{b}|}<0 \mid \quad[\because \vec{a} \cdot \vec{b}=|\vec{a}||\vec{b}| \cos \theta] \end{aligned}

\frac{\left(2 x^{2} \hat{i}+4 x \hat{j}+\hat{k}\right)(7 \hat{i}-2 \hat{j}+x \hat{k})}{\sqrt{\left(\left(2 x^{2}\right)^{2}+(4 x)^{2}+1^{2}\right)\left((7)^{2}+(-2)^{2}+x^{2}\right)}}<0

\begin{aligned} &\frac{14 x^{2}-8 x+x}{\sqrt{\left(4 x^{4}+16 x^{2}+1\right)\left(49+4+x^{2}\right)}}<0 \\\\ &14 x^{2}-7 x<0 \\\\ &7 x(2 x-1)<0 \\\\ &x<0 \; \; \; \; x<\frac{1}{2} \end{aligned}

Hence, option (b) is correct

 

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

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question