यदि \(\rm \vec{i} - a\vec{j} + 5\vec{k}\) और \(\rm 3\vec{i} - 6\vec{j} + b\vec{k}\) समानांतर सदिश हैं, तो b किसके बराबर है?

  1. 5
  2. 10
  3. 15
  4. 20

Answer (Detailed Solution Below)

Option 3 : 15
Free
Agniveer Navy SSR Full Test - 01
4.1 K Users
100 Questions 100 Marks 60 Mins

Detailed Solution

Download Solution PDF

संकल्पना:

यदि \({\rm{\vec a\;and\;\vec b}}\) एक-दूसरे के समानांतर दो सदिश हैं, तो \({\rm\vec{a} = λ \vec{b}}\) या \(\rm \vec{a} × \vec{b} =0\) है। 

गणना:

दिया गया है:

 \(\rm \vec{i} - a\vec{j} + 5\vec{k}\) और \(\rm 3\vec{i} - 6\vec{j} + b\vec{k}\) समानांतर सदिश हैं,

इसलिए, \(\rm \vec{i} - a\vec{j} + 5\vec{k}= λ (\rm 3\vec{i} - 6\vec{j} + b\vec{k})\)

 \(\rm \vec{i},\vec{j} \;and\; \vec{k}\)के गुणांक को बराबर करने पर 

⇒ 1 = 3λ, ∴ λ = 1/3            

⇒ -a = -6λ 

⇒ 5 = bλ                 .... (1)

समीकरण (1) में λ का मान रखने पर, हमें निम्न प्राप्त होता है 

5 = b × (1/3)

अतः b = 15

Latest Indian Navy Agniveer SSR Updates

Last updated on May 31, 2025

-> The Indian Navy SSR Agniveeer Merit List will be released soon on the official website.

-> The Indian Navy Agniveer SSR CBT Exam was conducted from 25th to 26th May 2025.

->The application window was open from 29th March 2025 to 16th April 2025.  

-> The Indian Navy SSR Agniveer Application Link is active on the official website of the Indian Navy.

.->Only unmarried males and females can apply for Indian Navy SSR Recruitment 2025.

-> The selection process includes a Computer Based Test, Written Exam, Physical Fitness Test (PFT), and  Medical Examination.

->Candidates Qualified in 10+2 with Mathematics & Physics from a recognized Board with a minimum 50% marks in aggregate can apply for the vacancy.

-> With a salary of Rs. 30,000, it is a golden opportunity for defence job seekers.

-> Candidates must go through the Indian Navy SSR Agniveer Previous Year Papers and Agniveer Navy SSR mock tests to practice a variety of questions for the exam.

More Types of Vectors Questions

More Vector Algebra Questions

Get Free Access Now
Hot Links: teen patti comfun card online teen patti plus teen patti master plus