Get detailed solutions for NCERT Class 11 Maths Chapter 11 Exercise 11.1
Master the fundamental concepts of three-dimensional geometry. Learn to identify the coordinates of points lying on the coordinate axes (Q.1) and coordinate planes (Q.2). Understand the concept of the eight octants and how to determine the octant of a given point based on the sign of its coordinates (Q.3). Complete the blanks related to basic 3D terminology (Q.4).
1. Coordinates of a Point on the $x$-axis
A point that lies directly on the $x$-axis has zero distance from both the $YZ$-plane and the $XZ$-plane.
- Its $y$-coordinate is 0.
- Its $z$-coordinate is 0.
A point on the $x$-axis has the form $(x, 0, 0)$.
2. Coordinates of a Point in the $XZ$-plane
The $XZ$-plane is the plane defined by the $x$-axis and the $z$-axis. Any point in this plane has zero distance from the $XZ$-plane itself.
- Its $y$-coordinate is 0.
A point in the $XZ$-plane has the form $(x, 0, z)$.
3. Name the Octants
The three coordinate planes ($XY$, $YZ$, $XZ$) divide the space into eight octants. The sign of the coordinates $(x, y, z)$ determines the octant.
| Octant | x-coordinate | y-coordinate | z-coordinate | Point Example |
| I | $+$ | $+$ | $+$ | $(1, 2, 3)$ |
| II | $-$ | $+$ | $+$ | $(-4, 2, 5)$ |
| III | $-$ | $-$ | $+$ | $(-3, -1, 6)$ |
| IV | $+$ | $-$ | $+$ | $(4, -2, 3)$ |
| V | $+$ | $+$ | $-$ | $(4, 2, -5)$ |
| VI | $-$ | $+$ | $-$ | $(-4, 2, -5)$ |
| VII | $-$ | $-$ | $-$ | $(-2, -4, -7)$ |
| VIII | $+$ | $-$ | $-$ | $(4, -2, -5)$ |
4. Fill in the Blanks
(i) The $x$-axis and $y$-axis taken together determine a plane known as $\mathbf{XY\text{-plane}}$.
(ii) The coordinates of points in the $XY$-plane are of the form $\mathbf{(x, y, 0)}$.
(iii) Coordinate planes divide the space into $\mathbf{8}$ octants.