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Chapters
2: Relations and Functions
3: Trigonometric Functions
4: Complex Numbers and Quadratic Equations
5: Linear Inequalities
6: Permutations and Combinations
7: Binomial Theorem
8: Sequences and Series
9: Straight Lines
10: Conic Sections
▶ 11: Introduction to Three Dimensional Geometry
12: Limits and Derivatives
13: Statistics
14: Probability
![NCERT solutions for Mathematics [English] Class 11 chapter 11 - Introduction to Three Dimensional Geometry - Shaalaa.com](/images/mathematics-english-class-11_6:6ab366e2671b448497dd3d3a0e6fed94.jpg "NCERT solutions for Mathematics [English] Class 11 chapter 11 - Introduction to Three Dimensional Geometry")
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Solutions for Chapter 11: Introduction to Three Dimensional Geometry
Below listed, you can find solutions for Chapter 11 of CBSE, Karnataka Board PUC NCERT for Mathematics [English] Class 11.
NCERT solutions for Mathematics [English] Class 11 11 Introduction to Three Dimensional Geometry EXERCISE 11.1 [Page 211]
A point is on the x-axis. What are its y-coordinates and z-coordinates?
A point is in the XZ-plane. What can you say about its y-coordinate?
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).
The x-axis and y-axis taken together determine a plane known as_______.
The coordinates of points in the XY-plane are of the form _______.
Coordinate planes divide the space into ______ octants.
NCERT solutions for Mathematics [English] Class 11 11 Introduction to Three Dimensional Geometry EXERCISE 11.2 [Page 213]
Find the distance between the pairs of points:
(2, 3, 5) and (4, 3, 1)
Find the distance between the following pairs of points:
(–3, 7, 2) and (2, 4, –1)
Find the distance between the following pairs of points:
(–1, 3, –4) and (1, –3, 4)
Find the distance between the following pairs of points:
(2, –1, 3) and (–2, 1, 3)
Show that the points (–2, 3, 5), (1, 2, 3) and (7, 0, –1) are collinear.
Verify the following:
(0, 7, –10), (1, 6, –6) and (4, 9, –6) are the vertices of an isosceles triangle.
Verify the following:
(0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of a right angled triangle.
Verify the following:
(–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are the vertices of a parallelogram.
Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).
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.
NCERT solutions for Mathematics [English] Class 11 11 Introduction to Three Dimensional Geometry Miscellaneous Exercise [Page 215]
Three vertices of a parallelogram ABCD are A (3, –1, 2), B (1, 2, –4) and C (–1, 1, 2). Find the coordinates of the fourth vertex.
Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0).
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.
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.
Solutions for 11: Introduction to Three Dimensional Geometry
NCERT solutions for Mathematics [English] Class 11 chapter 11 - Introduction to Three Dimensional Geometry
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Concepts covered in Mathematics [English] Class 11 chapter 11 Introduction to Three Dimensional Geometry are Coordinate Axes and Coordinate planes, Coordinates of a Point in Space, Distance Between Two Points, Section Formula, Three Dimessional Space, Coordinate Axes and Coordinate planes, Coordinates of a Point in Space, Distance Between Two Points, Section Formula, Three Dimessional Space.
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