Name the octants in which the following points lie: (1,2,3),…

Question 3 of 13beginner🔧 ApplyShort Answer2 marks

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

Correct Answer

To determine the octant, we observe the signs of the $x, y,$ and $z$ coordinates for each point. The point $(1,2,3)$ has signs $(+,+,+)$ , so it lies in Octant I. The point $(4,-2,3)$ has signs $(+,-,+)$ , placing it in Octant IV. The point $(4,-2,-5)$ has signs $(+,-,-)$ , so it lies in Octant VIII.

The point $(4,2,-5)$ has signs $(+,+,-)$ , placing it in Octant V. The point $(-4,2,-5)$ has signs $(-,+,-)$ , so it lies in Octant VI. The point $(-4,2,5)$ has signs $(-,+,+)$ , placing it in Octant II.

Finally, the point $(-3,-1,6)$ has signs $(-,-,+)$ , so it lies in Octant III. The point $(-2,-4,-7)$ has signs $(-,-,-)$ , placing it in Octant VII.

Exercise: EXERCISE 11.1 | Q: 3 | (Page Page 4)

For More Understanding

Explanation

The answer is derived from the sign convention table provided in the context. The table maps the signs of the x, y, and z coordinates to specific octants: I $(+,+,+)$ , II $(-,+,+)$ , III $(-,-,+)$ , IV $(+,-,+)$ , V $(+,+,-)$ , VI $(-,+,-)$ , VII $(-,-,-)$ , and VIII $(+,-,-)$ . By comparing the sign of each coordinate for every point with this table, the correct octant is identified.

Solution Steps

Step 1: Identify the signs of the coordinates $(x, y, z)$ for each given point.
Step 2: Match the identified signs with the octant sign table (e.g., $(+,+,+)$ corresponds to Octant I, $(-,-,-)$ corresponds to Octant VII).
Step 3: List the corresponding octant for each point based on the sign match.

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