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 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 9 maths textbook solution

Please solve RD Sharma class 12 chapter 26 Direction Cosines and Direction Ratios exercise Fill in the blanks question 9 maths textbook solution

Answers (1)

Final Answer:   5\sqrt{2}

Hint:

Length of projection =  Length ×  Direction cosine

Given:

Projections on coordinate axes are 3,4,5

To Find: 

Length of line segment

Solution:

Let Line segment PQ makes angle α,β,γ with x,y and z axes, such that length of projection in coordinate axes are:

\begin{aligned} &P Q \cos \alpha=3 \Rightarrow \cos \alpha=\frac{3}{P Q} \\ &P Q \cos \beta=4 \Rightarrow \cos \beta=\frac{4}{P Q} \\ &P Q \cos \gamma=5 \Rightarrow \cos \gamma=\frac{5}{P Q} \end{aligned}

Now by properties of direction cosine

\cos ^{2} \alpha+\cos ^{2} \beta+\cos ^{2} \gamma=1

\begin{aligned} &\therefore\left(\frac{3}{P Q}\right)^{2}+\left(\frac{4}{P Q}\right)^{2}+\left(\frac{5}{P Q}\right)^{2}=1 \\\\ &\frac{9}{P Q^{2}}+\frac{16}{P Q^{2}}+\frac{25}{P Q^{2}}=1 \\\\ &\frac{50}{P Q^{2}}=1 \end{aligned}

\begin{aligned} &P Q^{2}=50 \\\\ &P Q=\sqrt{50} \\\\ &P Q=5 \sqrt{2} \end{aligned}

Therefore, the total length of line segment is 5\sqrt{2}

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