NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2

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Get Free NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2 PDF in Hindi and English Medium. Introduction to three Dimensional Geometry Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Introduction to three Dimensional Geometry Ex 12.2 Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 12 Class 11 Introduction to three Dimensional Geometry Ex 12.2 provided in NCERT Textbook.

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NCERT Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.2

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry Ex 12.2
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry Ex 12.2

Question 1.
Find the distance between the following pairs of points:
(i) (2, 3, 5) and (4, 3, 1)
(ii) (-3, 7, 2) and (2, 4, -1)
(iii) (-1, 3, -4) and (1, -3, 4)
(iv) (2, -1, 3) and (-2, 1, 3)
Solution:
(i) The distance PQ between the points P(2, 3, 5) and Q(4, 3, 1) is
(PQ=sqrt { left( 4-2 right) ^{ 2 }+left( 3-3 right) ^{ 2 }left( 1-5 right) ^{ 2 } } )
= (sqrt { 4+0+16= } sqrt { 20 } =2sqrt { 5 } units.)

(ii) The distance PQ between the points P(-3, 7, 2) and Q(2, 4, -1) is
(PQ=sqrt { left[ 2-left( -3 right) right] ^{ 2 }+left( 4-7 right) ^{ 2 }left( -1-2 right) ^{ 2 } } )
(=sqrt { left( 2+3 right) ^{ 2 }+left( 4-7 right) ^{ 2 }+left( -1-2 right) ^{ 2 } } )
(=sqrt { 25+9+9 } =sqrt { 43 } units)

(iii) The distance PQ between the points P(-1, 3, -4) and Q(1, -3, 4) is
(PQ=sqrt { left[ 1-left( -1 right) right] ^{ 2 }+left( -3-3 right) ^{ 2 }left[ 4-left( -4 right) right] ^{ 2 } } )
(=sqrt { 4+36+64 } =sqrt { 104 } =2sqrt { 26 } units)

(iv) The distance PQ between the points P(2, -1, 3) and Q(-2, 1, 3) is
(PQ=sqrt { left( -2-2 right) ^{ 2 }+left[ 1-left( -1 right) right] ^{ 2 }+left( 3-3 right) ^{ 2 } } )
(=sqrt { 16+4+0 } =sqrt { 20 } =2sqrt { 5 } units)

Question 2.
Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear.
Solution:
Let A(-2, 3, 5), B(1, 2, 3) and C(7, 0, -1) be three given points.
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry 1
Now AC = AB + BC
Thus, points A, B and C are collinear.

Question 3.
Verify the following:
(i) (0, 7, -10), (1, 6, -6) and (4, 9, -6) are the vertices of an isosceles triangle.
(ii) (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of a right angled triangle.
(iii) (-1, 2, 1), (1, -2, 5), (4, -7,8) and (2, -3,4) are the vertices of a parallelogram.
Solution:
(i) Let A(0, 7, -10), B(l, 6, -6) and C(4, 9, -6) be three vertices of triangle ABC. Then
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry 2
Now, AB = BC
Thus, ABC is an isosceles triangle.

(ii) Let A(0, 7,10), B(-l, 6, 6) and C(-A, 9, 6) be three vertices of triangle ABC. Then
study rankers class 11 maths Chapter 12 Introduction to Three Dimensional Geometry 3
Now, AC2 = AB2 + BC2
Thus, ABC is a right angled triangle.

(iii) Let A(-1, 2, 1), B(1, -2, 5) and C(4, -7, 8) and D(2, -3,4) be four vertices of quadrilateral ABCD. Then
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry 4
Now AB = CD, BC = AD and AC ≠ BD
Thus A, B, C and D are vertices of a parallelogram ABCD.

Question 4.
Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, -1).
Solution:
Let A(x, y, z) be any point which is equidistant from points B(1, 2, 3) and C(3, 2, -1).
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry 5

Question 5.
Find the equation of the set of points P, the sum of whose distances from A(4, 0, 0) and B(-4,0,0) is equal to 10.
Solution:
Let P(x, y, z) be any point.
study rankers class 11 maths Chapter 12 Introduction to Three Dimensional Geometry 6
NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry 7

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