Name the octant in which (3, -4, 6) lies.

Answer

To determine the octant in which the point (3, -4, 6) lies, we will follow these steps:

### Step 1: Identify the coordinates
The coordinates of the point are given as (3, -4, 6). Here,
- x = 3
- y = -4
- z = 6

### Step 2: Determine the signs of the coordinates
Next, we will analyze the signs of each coordinate:
- The x-coordinate (3) is positive.
- The y-coordinate (-4) is negative.
- The z-coordinate (6) is positive.

### Step 3: Recall the octant definitions
In 3D space, the octants are defined based on the signs of the x, y, and z coordinates:
1. First Octant: ( +, +, + )
2. Second Octant: ( -, +, + )
3. Third Octant: ( -, -, + )
4. Fourth Octant: ( +, -, + )
5. Fifth Octant: ( +, +, - )
6. Sixth Octant: ( -, +, - )
7. Seventh Octant: ( -, -, - )
8. Eighth Octant: ( +, -, - )

### Step 4: Match the signs to the octants
Now, we will match the signs of our point (3, -4, 6) with the octants:
- x is positive (+)
- y is negative (-)
- z is positive (+)

From our definitions, we can see that the combination of signs ( +, -, + ) corresponds to the Fourth Octant.

### Conclusion
Therefore, the point (3, -4, 6) lies in the **Fourth Octant**.

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