Name the octant in which each of the following points lies:
$(i) (1, 2, 3)$
$(ii) (4, -2, 3)$
$(iii) (4, -2, -5)$
$(iv) (4, 2, -5)$
$(v) (-4, 2, 5)$
$(vi) (-3, -1, 6)$
$(vii) (2, -4, -7)$
$(viii) (-4, 2, -5)$

(N/A) The octants are determined by the signs of the coordinates $(x, y, z)$ as follows:

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.