Question:
In which octant does each of the given points lie?
(i) $(-4,-1,-6)$
(ii) $(2,3,-4)$
(iii) $(-6,5,-1)$
(iv) $(4,-3,-2)$
(v) $(-1,-6,5)$
(vi) $(4,6,8)$
Solution:
The position of a point in a octant is signified by the signs of the x, y, z coordinates.
Here is a table showing signs of the x, y, z coordinates in all the octants.
According to the table
(i) $(-4,-1,-6)$ lies in octant VII
(ii) $(2,3,-4)$ lies in octant $\mathrm{V}$
(iii) $(-6,5,-1)$ lies in octant VI
(iv) $(4,-3,-2)$ lies in octant VIII
(v) $(-1,-6,5)$ lies in octant III
(vi) $(4,6,8)$ lies in octant I