Question

Name the octants in which the following points lie:
$(1,2,3),(4,-2,3)(4,-2,-5),(4,2,-5),(-4,2,-5),(-4,2,5),(-3,-1,6),(2,-4,-7)$

Answer 1

The $x$-coordinate $y$-coordinate and$z$-coordinate of point $(1,2,3)$ are all positive.
Therefore this point lies in octant I

The $x$-coordinate $y$-coordinate and $z$-coordinate of point $(4,-2,3)$ are positive
negative and positive respectively. Therefore this point lies in octant IV

The $x$-coordinate $y$-coordinate and $z$-coordinate of point $(4,-2,-5)$ are positive
negative and negative respectively. Therefore this point lies in octant VIII

The $x$-coordinate, $y$-coordinate and $z$-coordinate of point $(4,2,-5)$ are positive
positive and negative respectively. Therefore this point lies in octant V

The $x$-coordinate, $y$-coordinate and $z$-coordinate of point $(-4,2,-5)$ are negative
positive, and negative respectively. Therefore this point lies in octant VI

The $x$-coordinate, $y$-coordinate and $z$-coordinate of point $(-4,2,5)$ are negative
positive and positive respectively. Therefore this point lies in octant II

The $x$-coordinate $y$-coordinate and $z$-coordinate of point $(-3,-1,6)$ are negative
negative and positive respectively. Therefore this point lies in octant III

The $x$-coordinate, $y$-coordinate and $z$-coordinate of point $(2,-4,-7)$ are positive
negative and negative respectively. Therefore this point lies in octant VIII