Anand Classes provides complete NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry Exercise 11.1, designed to help students understand the basics of 3D coordinate geometry with clarity. These step-by-step solutions are prepared according to the latest CBSE and NCERT guidelines, covering essential topics like coordinate axes, coordinate planes, and the position of points in space. Each question is solved systematically to make concepts easy and exam-ready. Click the print button to download study material and notes.
NCERT Question.1 : A point is on the x-axis. What are its y-coordinate and z-coordinate?
Solution:
If a point is on the x-axis, then its coordinates of $y$ and $z$ are zero.
Hence, the point is $(x, 0, 0)$.
Related topics: 3D coordinate geometry basics, Cartesian coordinates, x-axis representation, Class 11 Maths concepts.
NCERT Question.2 : A point is in the XZ-plane. What can you say about its y-coordinate?
Solution:
If a point lies in the XZ-plane, then its $y$-coordinate is zero.
Hence, the point is of the form $(x, 0, z)$.
Related topics: Coordinate planes in 3D, XZ-plane concept, y-coordinate zero points, NDA Maths preparation.
NCERT Question.3 : Name the octants in which the following points lie:
$$(1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), $$ $$(-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (2, -4, -7)$$
Solution :
The sign of the coordinates of a point determine the octant in which the
point lies. The following table shows the signs of the coordinates in eight octants :
| Octant | I | II | III | IV | V | VI | VII | VIII |
|---|---|---|---|---|---|---|---|---|
| x | + | – | – | + | + | – | – | + |
| y | + | + | – | – | + | + | – | – |
| z | + | + | + | + | – | – | – | – |
Now, determining the octants:
(i) $(1, 2, 3)$ → $x, y, z$ all positive → I octant
(ii) $(4, -2, 3)$ → $x$ positive, $y$ negative, $z$ positive → IV octant
(iii) $(4, -2, -5)$ → $x$ positive, $y$ negative, $z$ negative → VIII octant
(iv) $(4, 2, -5)$ → $x$ positive, $y$ positive, $z$ negative → V octant
(v) $(-4, 2, -5)$ → $x$ negative, $y$ positive, $z$ negative → VI octant
(vi) $(-4, 2, 5)$ → $x$ negative, $y$ positive, $z$ positive → II octant
(vii) $(-3, -1, 6)$ → $x, y$ negative, $z$ positive → III octant
(viii) $(2, -4, -7)$ → $x$ positive, $y, z$ negative → VIII octant
Related topics: Octants in 3D geometry, signs of coordinates, Class 11 coordinate geometry, JEE and CUET Maths preparation.
NCERT Question.4 : Fill in the blanks:
(i) The x-axis and y-axis taken together determine a plane known as …………..
(ii) The coordinates of points in the XY-plane are of the form…………….
(iii) Coordinate planes divide the space into ………..octants.
Solution :
(i) The x-axis and y-axis taken together determine a plane known as XY-plane.
(ii) The coordinates of points in the XY-plane are of the form $(x, y, 0)$.
(iii) Coordinate planes divide the space into eight octants.
Related topics: Coordinate planes (XY, YZ, ZX), 3D space division, Cartesian system, NCERT Class 11 Maths solutions.
For more detailed NCERT Maths solutions and 3D Geometry notes, visit Anand Classes — best for Class 11 Maths, JEE Main, NDA, and CUET preparation.
