Find the distance of the point P(3, 4, 6) from y-axis.

Answer

To find the distance of the point P(3, 4, 6) from the y-axis, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Position of the Point**:
The point P is given as P(3, 4, 6). In three-dimensional space, the coordinates represent (x, y, z) where:
- x = 3
- y = 4
- z = 6

2. **Identify the y-axis**:
The y-axis in three-dimensional space is represented by all points where x = 0 and z = 0. Therefore, any point on the y-axis can be represented as (0, y, 0).

3. **Distance Formula**:
The distance from a point (x1, y1, z1) to the y-axis can be calculated using the formula:
\[ d = \sqrt{(x_1 - 0)^2 + (z_1 - 0)^2} \]
This simplifies to:
\[ d = \sqrt{x_1^2 + z_1^2} \]

4. **Substituting the Values**:
For the point P(3, 4, 6):
- x1 = 3
- z1 = 6

Substitute these values into the distance formula:
\[ d = \sqrt{3^2 + 6^2} \]

5. **Calculating the Squares**:
Calculate \(3^2\) and \(6^2\):
- \(3^2 = 9\)
- \(6^2 = 36\)

6. **Adding the Squares**:
Now add the squares:
\[ d = \sqrt{9 + 36} = \sqrt{45} \]

7. **Simplifying the Square Root**:
The square root of 45 can be simplified:
\[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} \]

8. **Final Answer**:
Therefore, the distance of the point P(3, 4, 6) from the y-axis is:
\[ d = 3\sqrt{5} \]