The length of the foot of perpendicular drawn from
point (3, 4, 5) on z-axis is

Options

A. 5 units
B. `sqrt(34)` units
C. `sqrt(41)` units
D. `2sqrt(5)` units

Answer

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

### Step 1: Understand the Geometry
The z-axis is defined by the points where x = 0 and y = 0. Therefore, any point on the z-axis can be represented as (0, 0, z).

### Step 2: Identify the Coordinates
The given point is P(3, 4, 5). We need to find the perpendicular distance from this point to the z-axis.

### Step 3: Use the Formula for Distance
The formula to calculate the distance from a point (x₁, y₁, z₁) to the z-axis is given by:
\[ \text{Distance} = \sqrt{x^2 + y^2} \]
where (x, y) are the coordinates of the point.

### Step 4: Substitute the Coordinates
Substituting the coordinates of point P(3, 4, 5) into the formula:
\[ \text{Distance} = \sqrt{3^2 + 4^2} \]

### Step 5: Calculate the Squares
Calculate the squares of the coordinates:
\[ 3^2 = 9 \]
\[ 4^2 = 16 \]

### Step 6: Add the Squares
Now, add the squares:
\[ 9 + 16 = 25 \]

### Step 7: Take the Square Root
Finally, take the square root of the sum:
\[ \text{Distance} = \sqrt{25} = 5 \]

### Conclusion
The length of the foot of the perpendicular drawn from the point (3, 4, 5) on the z-axis is 5 units.

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