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 27 Straight Line in Space Exercise 27.2 Question 26 Maths Textbook Solution.

Explain Solution R.D.Sharma Class 12 Chapter 27 Straight Line in Space Exercise 27.2 Question 26 Maths Textbook Solution.

Answers (1)

Answer: the required vector equation is \vec{r}=(\hat{i}+\hat{j}+\hat{k})+\lambda(-4 \hat{i}+4 \hat{j}-\hat{k})

 

Given: find the vector and Cartesian equation of the line which is perpendicular to the lines with the equation

\frac{x+2}{1}=\frac{y-3}{2}=\frac{z+1}{2}and \: \frac{x-1}{2}=\frac{y-2}{3}

                =         \frac{z-3}{4}     and passes through the points (1,1,1). Also find the angle between the given lines

Hint: for showing perpendicular dot product must be equal to ‘0’

Solution: let the cartesian equation of the line passing through the point (1,1,1) will be

\frac{x-1}{a}=\frac{y-1}{b}=\frac{z-1}{c}

Now parallel vectors are  \bar{b_{1}},\bar{b_{2}},\bar{b_{3}}                                                                                                                                                       

From the question,

 \begin{aligned} &\vec{b}_{1}=\hat{a} \hat{i}+b \hat{j}+c \hat{k} \\ &\overrightarrow{b_{2}}=\hat{i}+2 \hat{j}+4 \hat{k} \text { Here } \\ &\overrightarrow{b_{3}}=2 \hat{i}+3 \hat{j}+4 \hat{k} \end{aligned}

                 \begin{aligned} &a+2 b+4 c=0 \ldots .(\mathrm{lV}) \\ &2 a+3 b+4 c=0 \ldots \ldots(\mathrm{V}) \end{aligned}

                  Solving (iv) and (v) we get

                   \begin{aligned} &\frac{a}{8-12}=\frac{b}{8-4}=\frac{c}{3-4} \\ &\therefore \frac{a}{-4}=\frac{b}{4}=\frac{c}{-1}=\lambda \end{aligned} 

               Therefore a=4\lambda ,b=4\lambda ,c=-\lambda

Now putting the above makes in equation;

  \begin{aligned} &\frac{x-1}{-4 \lambda}=\frac{y-1}{4 \lambda}=\frac{z-1}{-\lambda} \\ &\frac{x-1}{-4}=\frac{y-1}{4}=\frac{z-1}{-1} \end{aligned}           hence the vector equation is \vec{r}=(\hat{i}+\hat{j}+\hat{k})+\lambda(-4 \hat{i}+4 \hat{j}-\hat{k}).

 

 

 

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

Board Exam Time Table 2025 Live: UP Board exams from February 24; CBSE, BSEB date sheet soon
anam-khan

CBSE Date Sheet 2025 Live: Class 10, 12 board exam dates soon; syllabus, sample papers
anam-khan

Extra time in CBSE exams for students with type 1 diabetes: Kerala SHRC seeks report on plea

Latest Question