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 27 Straight Line in Space exercise Multiple choice question 4 maths

Explain solution RD Sharma class 12 chapter 27 Straight Line in Space exercise Multiple choice question 4 maths

Answers (1)

Answer: Correct answer is C.

Hint: Use vector dot product.

 

Given: : \frac{x-1}{1}=\frac{y-1}{1}=\frac{z-1}{2} \text { and } \frac{x-1}{-\sqrt{3}-1}=\frac{y-1}{\sqrt{3}-1}=\frac{z-1}{4}

 

Solution: The direction ratios of the given lines are proportional to 1 ,1, 2 and --\sqrt{3}-1, \sqrt{3}-1,4

The given lines are parallel to the vectors

\Rightarrow \overrightarrow{b_{1}}=\hat{\imath}+\hat{\jmath}+2 \widehat{k} \text { and } \overrightarrow{b_{2}}=(-\sqrt{3}-1) \hat{\imath}+(\sqrt{3}-1) \hat{\jmath}+4 \hat{k}

Let θ be the angle between the given lines.

Now,

\begin{aligned} &\operatorname{Cos} \theta=\frac{\overrightarrow{b_{1}} \cdot \overrightarrow{b_{2}}}{\left|\overrightarrow{b_{1}}\right|\left|\overrightarrow{b_{2}}\right|} \\\\ &\operatorname{Cos} \theta=\frac{(\hat{\imath}+\hat{\jmath}+2 \hat{k}) \cdot\{(-\sqrt{3}-1) \hat{\imath}+(\sqrt{3}-1) \hat{\jmath}+4 \hat{k}\}}{\sqrt{1^{2}+1^{2}+2^{2}} \sqrt{(-\sqrt{3}-1)^{2}+(\sqrt{3}-1)^{2}+(4)^{2}}} \end{aligned}

\begin{aligned} &\operatorname{Cos} \theta=\frac{-\sqrt{3}-1+\sqrt{3}-1+8}{\sqrt{3} \sqrt{24}} \\\\ &\operatorname{Cos} \theta=\frac{6}{6 \sqrt{2}} \end{aligned}

\begin{aligned} &\operatorname{Cos} \theta=\frac{1}{\sqrt{2}} \\\\ &\theta=\frac{\pi}{3} \end{aligned}

So, the correct option is  \text { (c) } \frac{\pi}{3}

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