# Class 11 Maths NCERT Solutions for Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.1

### Three Dimensional Geometry Exercise 12.1 Solutions

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

**Solution**

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

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

**Solution**

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

**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 x-coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive. Therefore, this point lies in octant I.

The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, 3) are positive, negative, and positive respectively. Therefore, this point lies in octant IV.

The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, –5) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII.

The x-coordinate, y-coordinate, and z-coordinate of point (4, 2, –5) are positive, positive, and negative respectively. Therefore, this point lies in octant V.

The x-coordinate, y-coordinate, and z-coordinate of point (–4, 2, –5) are negative, positive, and negative respectively. Therefore, this point lies in octant VI.

The x-coordinate, y-coordinate, and z-coordinate of point (–4, 2, 5) are negative, positive, and positive respectively. Therefore, this point lies in octant II.

The x-coordinate, y-coordinate, and z-coordinate of point (–3, –1, 6) are negative, negative, and positive respectively. Therefore, this point lies in octant III.

The x-coordinate, y-coordinate, and z-coordinate of point (2, –4, –7) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII.

**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.