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Question

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


Solution

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   

Mathematics
NCERT
Standard XI

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