Question

In which octant does $\left( { - 4,2,3} \right)$ lie?

Answer 1

Hint: To solve this question, we need to clearly write the 8 octants starting from all the coordinates being positive (anti-clockwise) in a tabular form as given below:

OCTANT	$x$	$y$	$z$
First	$ + $	$ + $	$ + $
Second	$ - $	$ + $	$ + $
Third	$ - $	$ - $	$ + $
Fourth	$ + $	$ - $	$ + $
Fifth	$ + $	$ - $	$ - $
Sixth	$ - $	$ - $	$ - $
Seventh	$ - $	$ + $	$ - $
Eighth	$ + $	$ + $	$ - $

Complete answer:
The given point is $\left( { - 4,2,3} \right)$
A coordinate system can be 2-dimensional or 3-dimensional. A 2-D coordinate system will have 4 quadrants and a 3-D coordinate system will have 8 octants. By convention, the first quadrant is the one where all the three coordinates are positive.

OCTANT	$x$	$y$	$z$
First	$ + $	$ + $	$ + $
Second	$ - $	$ + $	$ + $
Third	$ - $	$ - $	$ + $
Fourth	$ + $	$ - $	$ + $
Fifth	$ + $	$ - $	$ - $
Sixth	$ - $	$ - $	$ - $
Seventh	$ - $	$ + $	$ - $
Eighth	$ + $	$ + $	$ - $

Using the above table, we can find out which octant does the point lie in.
$x$ - coordinate: -4
$y$ - coordinate: 2
$z$ - coordinate: 3

Since $x$ coordinate is negative and the other two coordinates are greater than zero. Therefore, we can tell that $\left( { - 4,2,3} \right)$ is in the second octant.

Therefore, the correct option is D

Note: In a two-dimensional coordinate system there are two axes – x and y. In a three-dimensional coordinate system there are three axes-x, y, z. An octant is one division out of the eight divisions in the 3-D coordinate system which are defined by signs of the coordinates.