Name the octant in which each of the following points lies:
$(i) (1, 2, 3)$
$(ii) (4, -2, 3)$
$(iii) (4, -2, -5)$
$(iv) (4, 2, -5)$
$(v) (-4, 2, 5)$
$(vi) (-3, -1, 6)$
$(vii) (2, -4, -7)$
$(viii) (-4, 2, -5)$
$(i) (1, 2, 3)$
$(ii) (4, -2, 3)$
$(iii) (4, -2, -5)$
$(iv) (4, 2, -5)$
$(v) (-4, 2, 5)$
$(vi) (-3, -1, 6)$
$(vii) (2, -4, -7)$
$(viii) (-4, 2, -5)$
(N/A) The octants are determined by the signs of the coordinates $(x, y, z)$ as follows:
Based on the signs of the coordinates:
$(i) (1, 2, 3)$ lies in $I$ octant.
$(ii) (4, -2, 3)$ lies in $IV$ octant.
$(iii) (4, -2, -5)$ lies in $VIII$ octant.
$(iv) (4, 2, -5)$ lies in $V$ octant.
$(v) (-4, 2, 5)$ lies in $II$ octant.
$(vi) (-3, -1, 6)$ lies in $III$ octant.
$(vii) (2, -4, -7)$ lies in $VIII$ octant.
$(viii) (-4, 2, -5)$ lies in $VI$ octant.
| Octant | Signs $(x, y, z)$ |
| $I$ | $(+, +, +)$ |
| $II$ | $(-, +, +)$ |
| $III$ | $(-, -, +)$ |
| $IV$ | $(+, -, +)$ |
| $V$ | $(+, +, -)$ |
| $VI$ | $(-, +, -)$ |
| $VII$ | $(-, -, -)$ |
| $VIII$ | $(+, -, -)$ |
Based on the signs of the coordinates:
$(i) (1, 2, 3)$ lies in $I$ octant.
$(ii) (4, -2, 3)$ lies in $IV$ octant.
$(iii) (4, -2, -5)$ lies in $VIII$ octant.
$(iv) (4, 2, -5)$ lies in $V$ octant.
$(v) (-4, 2, 5)$ lies in $II$ octant.
$(vi) (-3, -1, 6)$ lies in $III$ octant.
$(vii) (2, -4, -7)$ lies in $VIII$ octant.
$(viii) (-4, 2, -5)$ lies in $VI$ octant.
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