• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • RBSE Model Papers
    • RBSE Class 12th Board Model Papers 2022
    • RBSE Class 10th Board Model Papers 2022
    • RBSE Class 8th Board Model Papers 2022
    • RBSE Class 5th Board Model Papers 2022
  • RBSE Books
  • RBSE Solutions for Class 10
    • RBSE Solutions for Class 10 Maths
    • RBSE Solutions for Class 10 Science
    • RBSE Solutions for Class 10 Social Science
    • RBSE Solutions for Class 10 English First Flight & Footprints without Feet
    • RBSE Solutions for Class 10 Hindi
    • RBSE Solutions for Class 10 Sanskrit
    • RBSE Solutions for Class 10 Rajasthan Adhyayan
    • RBSE Solutions for Class 10 Physical Education
  • RBSE Solutions for Class 9
    • RBSE Solutions for Class 9 Maths
    • RBSE Solutions for Class 9 Science
    • RBSE Solutions for Class 9 Social Science
    • RBSE Solutions for Class 9 English
    • RBSE Solutions for Class 9 Hindi
    • RBSE Solutions for Class 9 Sanskrit
    • RBSE Solutions for Class 9 Rajasthan Adhyayan
    • RBSE Solutions for Class 9 Physical Education
    • RBSE Solutions for Class 9 Information Technology
  • RBSE Solutions for Class 8
    • RBSE Solutions for Class 8 Maths
    • RBSE Solutions for Class 8 Science
    • RBSE Solutions for Class 8 Social Science
    • RBSE Solutions for Class 8 English
    • RBSE Solutions for Class 8 Hindi
    • RBSE Solutions for Class 8 Sanskrit
    • RBSE Solutions

RBSE Solutions

Rajasthan Board Textbook Solutions for Class 5, 6, 7, 8, 9, 10, 11 and 12

  • RBSE Solutions for Class 7
    • RBSE Solutions for Class 7 Maths
    • RBSE Solutions for Class 7 Science
    • RBSE Solutions for Class 7 Social Science
    • RBSE Solutions for Class 7 English
    • RBSE Solutions for Class 7 Hindi
    • RBSE Solutions for Class 7 Sanskrit
  • RBSE Solutions for Class 6
    • RBSE Solutions for Class 6 Maths
    • RBSE Solutions for Class 6 Science
    • RBSE Solutions for Class 6 Social Science
    • RBSE Solutions for Class 6 English
    • RBSE Solutions for Class 6 Hindi
    • RBSE Solutions for Class 6 Sanskrit
  • RBSE Solutions for Class 5
    • RBSE Solutions for Class 5 Maths
    • RBSE Solutions for Class 5 Environmental Studies
    • RBSE Solutions for Class 5 English
    • RBSE Solutions for Class 5 Hindi
  • RBSE Solutions Class 12
    • RBSE Solutions for Class 12 Maths
    • RBSE Solutions for Class 12 Physics
    • RBSE Solutions for Class 12 Chemistry
    • RBSE Solutions for Class 12 Biology
    • RBSE Solutions for Class 12 English
    • RBSE Solutions for Class 12 Hindi
    • RBSE Solutions for Class 12 Sanskrit
  • RBSE Class 11

RBSE Solutions for Class 12 Maths Chapter 14 त्रि – विमीयज्यामिति Ex 14.5

May 24, 2019 by Prasanna Leave a Comment

Rajasthan Board RBSE Class 12 Maths Chapter 14 त्रि – विमीयज्यामिति Ex 14.5

प्रश्न 1.
रेखाओं
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
और
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
के मध्य की न्यूनतम दूरी ज्ञात कीजिए।
हल :
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5

प्रश्न 2.
रेखाओं
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
के मध्य की न्यूनतम दूरी ज्ञात कीजिए।
हल :
रेखाओं
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
के बीच की न्यूनतम दूरी
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5

प्रश्न 3.
रेखाएँ, जिनके सदिश समीकरण निम्नलिखित है, के मध्य की न्यूनतम दूरी ज्ञात कीजिए
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
और
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
हल :
रेखाएँओं
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5

प्रश्न 4.
रेखाएँ, जिसकी सदिश समीकरण निम्नलिखित हैं, के मध्य की न्यूनतम दूरी ज्ञात कीजिए
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
और
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
हल :
रेखा
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5

प्रश्न 5.
निम्न रेखाओं के मध्य लघुत्तम दूरी ज्ञात कीजिए
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
तथा लघुतम दूरी वाली रेखा का समीकरण भी ज्ञात कीजिए।
हल :
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
अतः रेखा (1) पर कोई बिंदु P(2r1 + 1, 3r1 – 1, r1) तथा
रेखा (2) पर कोई बिंदु Q(3r2 – 1, r2 + 2, r2 + 2)
तब रेखा PQ के दिक्-अनुपात
= 3r2 – 2r1 – 2, r2 – 3r1 + 3, 2 – r1
PQ रेखा (1) के लम्बवत् हैं, इसलिए
a1a2 + b1b2 + c1c2 = 0
2(3r2 – 2r1 – 2) + 3(r2 – 3r1 + 3) + 1(2 – r1) = 0
9r2 – 14r1 = 7 …(3)
PQ रेखा (2) के लम्बवत् है।।
इसलिए a1a2 + b1b2 + c1c2 = 0
3(3r2 – 2r1 – 2) + 1(r2 – 3r1 + 3) + 0(2 – r1) = 0
10r2 – 9r1 – 3 = 0
समी. (3) व (4) को हल करने पर
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5
r1 व r2 के ये मान बिन्दु P व Q में रखने पर
RBSE Solutions for Class 12 Maths Chapter 14 त्रि - विमीयज्यामिति Ex 14.5

RBSE Solutions for Class 12 Maths

Share this:

  • Click to share on WhatsApp (Opens in new window)
  • Click to share on Twitter (Opens in new window)
  • Click to share on Facebook (Opens in new window)

Related

Filed Under: Class 12

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Primary Sidebar

Recent Posts

  • RBSE Solutions for Class 6 Maths Chapter 6 Decimal Numbers Additional Questions
  • RBSE Solutions for Class 11 Psychology in Hindi Medium & English Medium
  • RBSE Solutions for Class 11 Geography in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 Hindi
  • RBSE Solutions for Class 3 English Let’s Learn English
  • RBSE Solutions for Class 3 EVS पर्यावरण अध्ययन अपना परिवेश in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 Maths in Hindi Medium & English Medium
  • RBSE Solutions for Class 3 in Hindi Medium & English Medium
  • RBSE Solutions for Class 4 Hindi
  • RBSE Solutions for Class 4 English Let’s Learn English
  • RBSE Solutions for Class 4 EVS पर्यावरण अध्ययन अपना परिवेश in Hindi Medium & English Medium

Footer

RBSE Solutions for Class 12
RBSE Solutions for Class 11
RBSE Solutions for Class 10
RBSE Solutions for Class 9
RBSE Solutions for Class 8
RBSE Solutions for Class 7
RBSE Solutions for Class 6
RBSE Solutions for Class 5
RBSE Solutions for Class 12 Maths
RBSE Solutions for Class 11 Maths
RBSE Solutions for Class 10 Maths
RBSE Solutions for Class 9 Maths
RBSE Solutions for Class 8 Maths
RBSE Solutions for Class 7 Maths
RBSE Solutions for Class 6 Maths
RBSE Solutions for Class 5 Maths
RBSE Class 11 Political Science Notes
RBSE Class 11 Geography Notes
RBSE Class 11 History Notes

Copyright © 2023 RBSE Solutions

 

Loading Comments...