• Skip to main content
  • Skip to primary sidebar
  • Skip to footer
  • NCERT Solutions
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • GSEB Solutions
  • Maharashtra Board
  • Kerala Board
    • Kerala Syllabus 9th Standard Physics Solutions Guide
    • Kerala Syllabus 9th Standard Biology Solutions Guide
  • Goa Board

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 are part of NCERT Solutions for Class 12 Maths. Here we have given NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2.

  • Three Dimensional Geometry Class 12 Ex 11.1
  • Three Dimensional Geometry Class 12 Ex 11.3
Board CBSE
Textbook NCERT
Class Class 12
Subject Maths
Chapter Chapter 11
Chapter Name Three Dimensional Geometry
Exercise Ex 11.2
Number of Questions Solved 17
Category NCERT Solutions

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2

Ex 11.2 Class 12 Maths Question 1.
Show that the three lines with direction cosines:
\frac { 12 }{ 13 } ,\frac { -3 }{ 13 } ,\frac { -4 }{ 13 } ,\frac { 4 }{ 13 } ,\frac { 12 }{ 13 } ,\frac { 3 }{ 13 } ,\frac { 3 }{ 13 } ,\frac { -4 }{ 13 } ,\frac { 12 }{ 13 }
are mutually perpendicular.
Solution:
Let the lines be L1,L2 and L3.
∴ For lines L1 and L2
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q17.2

Ex 11.2 Class 12 Maths Question 2.
Show that the line through the points (1,-1,2) (3,4, -2) is perpendicular to the line through the points (0,3,2) and (3,5,6).
Solution:
Let A, B be the points (1, -1, 2), (3, 4, -2) respectively Direction ratios of AB are 2,5, -4
Let C, D be the points (0, 3, 2) and (3, 5, 6) respectively Direction ratios of CD are 3, 2,4 AB is Perpendicular to CD if
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q17.3

Ex 11.2 Class 12 Maths Question 3.
Show that the line through the points (4,7,8) (2,3,4) is parallel to the line through the points (-1,-2,1) and (1,2,5).
Solution:
Let the points be A(4,7,8), B (2,3,4), C (-1,-2,1) andD(1,2,5).
Now direction ratios of AB are
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q3.1

Ex 11.2 Class 12 Maths Question 4.
Find the equation of the line which passes through the point (1,2,3) and is parallel to the vector 3\hat { i } +2\hat { j } -2\hat { k }
Solution:
Equation of the line passing through the point
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q17.4

Ex 11.2 Class 12 Maths Question 5.
Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2\hat { i } -\hat { j } +4\hat { k } and is in the direction \hat { i } +2\hat { j } -\hat { k } .
Solution:
The vector equation of a line passing through a point with position vector \overrightarrow { a } and parallel to the
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q17.5
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q5.1

Ex 11.2 Class 12 Maths Question 6.
Find the cartesian equation of the line which passes through the point (-2,4, -5) and parallel to the line is given by \frac { x+3 }{ 3 } =\frac { y-4 }{ 5 } =\frac { z+8 }{ 6 }
Solution:
The cartesian equation of the line passing through the point (-2,4, -5) and parallel to the
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q6.1

Ex 11.2 Class 12 Maths Question 7.
The cartesian equation of a line is
\frac { x-5 }{ 3 } =\frac { y+4 }{ 7 } =\frac { z-6 }{ 2 }
write its vector form.
Solution:
The cartesian equation of the line is
\frac { x-5 }{ 3 } =\frac { y+4 }{ 7 } =\frac { z-6 }{ 2 }
Clearly (i) passes through the point (5, – 4, 6) and has 3,7,2 as its direction ratios.
=> Line (i) passes through the point A with
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q7.1

Ex 11.2 Class 12 Maths Question 8.
Find the vector and the cartesian equations of the lines that passes through the origin and (5,-2,3).
Solution:
The line passes through point
\therefore \overrightarrow { a } =\overrightarrow { 0 }
Direction ratios of the line passing through the
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q8.1

Ex 11.2 Class 12 Maths Question 9.
Find the vector and cartesian equations of the line that passes through the points (3, -2, -5), (3,-2,6).
Solution:
The PQ passes through the point P(3, -2, -5)
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q9.1

Ex 11.2 Class 12 Maths Question 10.
Find the angle between the following pair of lines
(i) \overrightarrow { r } =2\hat { i } -5\hat { j } +\hat { k } +\lambda (3\hat { i } +2\hat { j } +6\hat { k } )
and\quad \overrightarrow { r } =7\hat { i } -6\hat { j } +\mu (\hat { i } +2\hat { j } +2\hat { k } )
(ii) \overrightarrow { r } =3\hat { i } +\hat { j } -2\hat { k } +\lambda (\hat { i } -\hat { j } -2\hat { k } )
\overrightarrow { r } =2\hat { i } -\hat { j } -56\hat { k } +\mu (3\hat { i } -5\hat { j } -4\hat { k } )
Solution:
(i) Let θ be the angle between the given lines.
The given lines are parallel to the vectors
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q10.1

Ex 11.2 Class 12 Maths Question 11.
Find the angle between the following pair of lines
(i) \frac { x-2 }{ 2 } =\frac { y-1 }{ 5 } =\frac { z+3 }{ -3 } and\frac { x+2 }{ -1 } =\frac { y-4 }{ 8 } =\frac { z-5 }{ 4 }
(ii) \frac { x }{ 2 } =\frac { y }{ 2 } =\frac { z }{ 1 } and\frac { x-5 }{ 4 } =\frac { y-2 }{ 1 } =\frac { z-3 }{ 8 }
Solution:
Given
(i) \frac { x-2 }{ 2 } =\frac { y-1 }{ 5 } =\frac { z+3 }{ -3 } and\frac { x+2 }{ -1 } =\frac { y-4 }{ 8 } =\frac { z-5 }{ 4 }
(ii) \frac { x }{ 2 } =\frac { y }{ 2 } =\frac { z }{ 1 } and\frac { x-5 }{ 4 } =\frac { y-2 }{ 1 } =\frac { z-3 }{ 8 }
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q11.1

Ex 11.2 Class 12 Maths Question 12.
Find the values of p so that the lines
\frac { 1-x }{ 3 } =\frac { 7y-14 }{ 2p } =\frac { z-3 }{ 2 } and\frac { 7-7x }{ 3p } =\frac { y-5 }{ 1 } =\frac { 6-z }{ 5 }
are at right angles
Solution:
The given equation are not in the standard form
The equation of given lines is
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q12.1

Ex 11.2 Class 12 Maths Question 13.
Show that the lines \frac { x-5 }{ 7 } =\frac { y+2 }{ -5 } =\frac { z }{ 1 } and\frac { x }{ 1 } =\frac { y }{ 2 } =\frac { z }{ 3 } are perpendicular to each other
Solution:
Given lines
\frac { x-5 }{ 7 } =\frac { y+2 }{ -5 } =\frac { z }{ 1 } …(i)
\frac { x }{ 1 } =\frac { y }{ 2 } =\frac { z }{ 3 } …(ii)
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q13.1

Ex 11.2 Class 12 Maths Question 14.
Find the shortest distance between the lines
\overrightarrow { r } =(\hat { i } +2\hat { j } +\hat { k } )+\lambda (\hat { i } -\hat { j } +\hat { k } ) and
\overrightarrow { r } =(2\hat { i } -\hat { j } -\hat { k } )+\mu (2\hat { i } +\hat { j } +2\hat { k } )
Solution:
The shortest distance between the lines
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q14.1

Ex 11.2 Class 12 Maths Question 15.
Find the shortest distance between the lines
\frac { x+1 }{ 7 } =\frac { y+1 }{ -6 } =\frac { z+1 }{ 1 } and\frac { x-3 }{ 1 } =\frac { y-5 }{ -2 } =\frac { z-7 }{ 1 }
Solution:
Shortest distance between the lines
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q15.1

Ex 11.2 Class 12 Maths Question 16.
Find the distance between die lines whose vector equations are:
\overrightarrow { r } =(\hat { i } +2\hat { j } +3\hat { k) } +\lambda (\hat { i } -3\hat { j } +2\hat { k } ) and
\overrightarrow { r } =(4\hat { i } +5\hat { j } +6\hat { k) } +\mu (2\hat { i } +3\hat { j } +\hat { k } )
Solution:
Comparing the given equations with
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q16.1

Ex 11.2 Class 12 Maths Question 17.
Find the shortest distance between the lines whose vector equations are
\overrightarrow { r } =(1-t)\hat { i } +(t-2)\hat { j } +(3-2t)\hat { k } and
\overrightarrow { r } =(s+1)\hat { i } +(2s-1)\hat { j } -(2s+1)\hat { k }
Solution:
Comparing these equation with
NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 Q17.1

We hope the NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2 help you. If you have any query regarding NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Ex 11.2, drop a comment below and we will get back to you at the earliest.

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers

Recent Posts

  • MCQ Questions for Class 8 Science Chapter 18 Pollution of Air and Water with Answers
  • MCQ Questions for Class 8 Science Chapter 17 Stars and the Solar System with Answers
  • MCQ Questions for Class 8 Science Chapter 16 Light with Answers
  • MCQ Questions for Class 8 Science Chapter 15 Some Natural Phenomena with Answers
  • MCQ Questions for Class 8 Science Chapter 14 Chemical Effects of Electric Current with Answers
  • MCQ Questions for Class 8 Science Chapter 13 Sound with Answers
  • MCQ Questions for Class 8 Science Chapter 12 Friction with Answers
  • MCQ Questions for Class 8 Science Chapter 11 Force and Pressure with Answers
  • MCQ Questions for Class 8 Science Chapter 10 Reaching the Age of Adolescence with Answers
  • MCQ Questions for Class 8 Science Chapter 9 Reproduction in Animals with Answers
  • MCQ Questions for Class 8 Science Chapter 8 Cell Structure and Functions with Answers
  • MCQ Questions for Class 8 Science Chapter 7 Conservation of Plants and Animals with Answers
  • MCQ Questions for Class 8 Science Chapter 6 Combustion and Flame with Answers
  • MCQ Questions for Class 8 Science Chapter 5 Coal and Petroleum with Answers
  • MCQ Questions for Class 8 Science Chapter 4 Materials: Metals and Non-Metals with Answers

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions