In which octant does each of the given points lie?
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