NCERT Solutions for Class 11 Maths Maths Chapter 12

Introduction to Three Dimensional Geometry Class 11

Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.1, 12.2, 12.3, miscellaneous Solutions

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Exercise 12.1 : Solutions of Questions on Page Number : 271

Q1 :  

A point is on the x-axis. What are its y-coordinates and z-coordinates?


Answer :

If a point is on the x-axis, then its y-coordinates and z-coordinates are zero.

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Q2 :  

A point is in the XZ-plane. What can you say about its y-coordinate?


Answer :

If a point is in the XZ plane, then its y-coordinate is zero.

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Q3 :  

Name the octants in which the following points lie:

(1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5),

(-3, -1, 6), (2, -4, -7)


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Q4 :  

Fill in the blanks:


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Exercise 12.2 : Solutions of Questions on Page Number : 273

Q1 :  

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)


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Q2 :  

Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear.


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Q3 :  

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.


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Q4 :  

Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, -1).


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Q5 :  

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.


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Exercise 12.3 : Solutions of Questions on Page Number : 277

Q1 :  

Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) in the ratio (i) 2:3 internally, (ii) 2:3 externally.


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Q2 :  

Given that P (3, 2, -4), Q (5, 4, -6) and R (9, 8, -10) are collinear. Find the ratio in which Q divides PR.


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Q3 :  

Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8).


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Q4 :  

Using section formula, show that the points A (2, –3, 4), B (–1, 2, 1) and are collinear.


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Q5 :  

Find the coordinates of the points which trisect the line segment joining the points P (4, 2, -6) and Q (10, -16, 6).


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Exercise Miscellaneous : Solutions of Questions on Page Number : 278

Q1 :  

Three vertices of a parallelogram ABCD are A (3, -1, 2), B (1, 2, -4) andC (-1, 1, 2). Find the coordinates of the fourth vertex.


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Q2 :  

Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0).


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Q3 :  

If the origin is the centroid of the triangle PQR with vertices P (2a, 2, 6), Q (-4, 3b, -10) and R (8, 14, 2c), then find the values of a, b and c.


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Q4 :  

Find the coordinates of a point on y-axis which are at a distance offrom the point P (3, –2, 5).


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Q5 :  

A point R with x-coordinate 4 lies on the line segment joining the pointsP (2, –3, 4) and Q (8, 0, 10). Find the coordinates of the point R.

[Hint suppose R divides PQ in the ratio k: 1. The coordinates of the point R are given by


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Q6 :  

If A and B be the points (3, 4, 5) and (-1, 3, -7), respectively, find the equation of the set of points P such that PA2 + PB2 = k2, where k is a constant.


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Maths - Maths : CBSE NCERT Exercise Solutions for Class 11th for Introduction to Three Dimensional Geometry ( Exercise 12.1, 12.2, 12.3, miscellaneous ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

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