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:

Here is the table which represents the octants in three-dimensional geometry:

(i) (1, 2, 3)

Here x is positive, y is positive, and z is positive. So, it lies in octant I .

(ii) (4, - 2, 3)

Here x is positive, y is negative, and z is positive. So, it lies in octant IV.

(iii) (4, - 2, - 5)

Here x is positive, y is negative, and z is negative. So, it lies in octant VIII .

(iv) (4, 2, - 5)

Here x is positive, y is positive, and z is negative. So, it lies in octant V .

(v) (- 4, 2, - 5)

Here x is negative, y is positive, and z is negative. So, it lies in octant VI.

(vi) (- 4, 2, 5)

Here x is negative, y is positive, and z is positive. So, it lies in octant II.

(vii) (- 3, - 1, 6)

Here x is negative, y is negative, and z is positive. So, it lies in octant III.

(viii) (2, - 4, -7)

Here x is positive, y is negative, and z is negative. So, it lies in octant VIII

NCERT Solutions Class 11 Maths Chapter 12 Exercise 12.1 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).

Summary:

(1, 2, 3) lies in the octant I.
(4, - 2, 3) lies in the octant IV.
(4, - 2, - 5) lies in the octant VIII.
(4, 2, - 5) lies in the octant V.
(- 4, 2, - 5) lies in the octant VI.
(- 4, 2, 5) lies in the octant II.
(- 3, - 1, 6) lies in the octant III.
(2, - 4, -7) lies in the octant VII.