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 1: Understand the Coordinates
The point P is given as P(3, 4, 6), where:
- x-coordinate = 3
- y-coordinate = 4
- z-coordinate = 6

### Step 2: Identify the Formula for Distance from the y-axis
The distance of a point (x, y, z) from the y-axis can be calculated using the formula:
\[ \text{Distance} = \sqrt{x^2 + z^2} \]
This is because the y-axis is defined by x = 0 and z = 0.

### Step 3: Substitute the Coordinates into the Formula
Now, we substitute the x and z coordinates of point P into the formula:
\[ \text{Distance} = \sqrt{3^2 + 6^2} \]

### Step 4: Calculate the Squares
Calculate \(3^2\) and \(6^2\):
- \(3^2 = 9\)
- \(6^2 = 36\)

### Step 5: Add the Squares
Now, add these two values:
\[ 9 + 36 = 45 \]

### Step 6: Take the Square Root
Now, take the square root of the sum:
\[ \text{Distance} = \sqrt{45} \]

### Step 7: Simplify the Square Root
We can simplify \(\sqrt{45}\):
\[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} \]

### Final Answer
Thus, the distance of the point P(3, 4, 6) from the y-axis is:
\[ 3\sqrt{5} \]

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