Question

Name the octant in which the following point lie \[{\text{(4, - 3,5)}}\]

Answer 1

Hint: First we need to draw the octant coordinate and then we have to move in anticlockwise direction by marking of it’s sign as the following table for octant can be given as:

Octants	X	Y	Z
1	+	+	+
2	-	+	+
3	-	-	+
4	+	-	+
5	+	-	-
6	-	-	-
7	-	+	-
8	+	+	-

Complete step-by-step answer:
The given point is \[{\text{(4, - 3,5)}}\].
We should first define octant. Just as the two-dimensional coordinates system can be divided into four quadrants the three-dimensional coordinate system can be divided into eight octants. The first octant is the octant in which all three of the coordinates are positive.

Octants	X	Y	Z
1	+	+	+
2	-	+	+
3	-	-	+
4	+	-	+
5	+	-	-
6	-	-	-
7	-	+	-
8	+	+	-

Now, look at the sign of the given number and match it with the octants as per drawn in the table.
 Hence our answer is fourth octant.
Note: An octant in solid geometry is one of the eight divisions of a Euclidean three-dimensional coordinate system defined by the signs of the coordinates. It is similar to the two-dimensional quadrant and the one-dimensional ray. There are eight octants in a three-dimensional coordinate system. In a three-dimensional coordinate system, the x-axis, y-axis, and z-axis.