The length of the perpendicular drawn from the point `P(3,4,5)` on y-axis is

Options

A. `sqrt41`
B. `sqrt34`
C. 5
D. none of these

Explanation

To find the length of the perpendicular drawn from the point \( P(3, 4, 5) \) to the y-axis, we can follow these steps:

### Step 1: Identify the coordinates of the point on the y-axis
The y-axis can be represented by points of the form \( (0, y, 0) \). Since we are looking for the perpendicular from point \( P(3, 4, 5) \) to the y-axis, we need to find the point on the y-axis that has the same y-coordinate as point \( P \).

### Step 2: Determine the coordinates of the point on the y-axis
The coordinates of the point on the y-axis that corresponds to point \( P \) will be \( A(0, 4, 0) \).

### Step 3: Use the distance formula
To find the length of the perpendicular, we can use the distance formula between the two points \( P(3, 4, 5) \) and \( A(0, 4, 0) \). The distance \( d \) is given by:

\[ d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 + (z_1 - z_2)^2} \]

Where:
- \( (x_1, y_1, z_1) = (3, 4, 5) \)
- \( (x_2, y_2, z_2) = (0, 4, 0) \)

### Step 4: Substitute the coordinates into the distance formula
Substituting the coordinates into the formula, we get:

\[ d = \sqrt{(3 - 0)^2 + (4 - 4)^2 + (5 - 0)^2} \]

### Step 5: Simplify the expression
Calculating each term:

\[ d = \sqrt{3^2 + 0^2 + 5^2} = \sqrt{9 + 0 + 25} = \sqrt{34} \]

### Step 6: Conclusion
Thus, the length of the perpendicular drawn from point \( P(3, 4, 5) \) to the y-axis is:

\[ \sqrt{34} \text{ units} \]

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