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)`.

Explanation

To determine the octants in which the given points lie, we need to analyze 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 x, y, and z coordinates. Here’s a breakdown of the octants:

1. **First Octant**: (x > 0, y > 0, z > 0)
2. **Second Octant**: (x < 0, y > 0, z > 0)
3. **Third Octant**: (x < 0, y < 0, z > 0)
4. **Fourth Octant**: (x > 0, y < 0, z > 0)
5. **Fifth Octant**: (x > 0, y > 0, z < 0)
6. **Sixth Octant**: (x < 0, y > 0, z < 0)
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