Find the octant in which the following points lie
(i) (-3,1,-2)
(ii) (3,1,-2)
(iii) (-3,1,-2)
(iv) (-3,-1,-2)

Answer

To determine the octant in which each of the given points lies, we need to consider the signs of the coordinates (x, y, z) for each point. The three-dimensional space is divided into eight octants based on the signs of the coordinates.

### Step-by-Step Solution:

1. **Understanding Octants**:
- The three-dimensional space is divided into eight octants based on the signs of the x, y, and z coordinates.
- The octants are defined as follows:
- Octant I: ( +, +, + )
- Octant II: ( -, +, + )
- Octant III: ( -, -, + )
- Octant IV: ( +, -, + )
- Octant V: ( +, +, - )
- Octant VI: ( -, +, - )
- Octant VII: ( -, -, - )
- Octant VIII: ( +, -, - )

2. **Analyzing Each Point**:
- **Point (i): (-3, 1, -2)**
- x = -3 (negative)
- y = 1 (positive)
- z = -2 (negative)
- This corresponds to Octant VI ( -, +, - ).

- **Point (ii): (3, 1, -2)**
- x = 3 (positive)
- y = 1 (positive)
- z = -2 (negative)
- This corresponds to Octant V ( +, +, - ).

- **Point (iii): (-3, 1, -2)**
- x = -3 (negative)
- y = 1 (positive)
- z = -2 (negative)
- This is the same as Point (i) and corresponds to Octant VI ( -, +, - ).

- **Point (iv): (-3, -1, -2)**
- x = -3 (negative)
- y = -1 (negative)
- z = -2 (negative)
- This corresponds to Octant VII ( -, -, - ).

### Summary of Results:
- Point (i): (-3, 1, -2) → Octant VI
- Point (ii): (3, 1, -2) → Octant V
- Point (iii): (-3, 1, -2) → Octant VI
- Point (iv): (-3, -1, -2) → Octant VII