Force `3N, 4N` and `12 N` act at a point in mutually perpendicular directions. The magnetitude of the resultant resultant force us :-

Options

A. `19 N`
B. `13 N`
C. `11 N`
D. `5 N`

Explanation

To find the magnitude of the resultant force when three forces of 3N, 4N, and 12N act at a point in mutually perpendicular directions, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces**:
Let the forces be:
- \( F_1 = 3 \, \text{N} \)
- \( F_2 = 4 \, \text{N} \)
- \( F_3 = 12 \, \text{N} \)

2. **Use the Pythagorean Theorem**:
Since the forces are acting in mutually perpendicular directions, we can calculate the resultant force using the formula:
\[ R = \sqrt{F_1^2 + F_2^2 + F_3^2} \]

3. **Calculate Each Force's Square**:
- \( F_1^2 = 3^2 = 9 \)
- \( F_2^2 = 4^2 = 16 \)
- \( F_3^2 = 12^2 = 144 \)

4. **Sum the Squares**:
Now, add these squares together:
\[ 9 + 16 + 144 = 169 \]

5. **Take the Square Root**:
Finally, take the square root of the sum to find the resultant force:
\[ R = \sqrt{169} = 13 \, \text{N} \]

### Conclusion:
The magnitude of the resultant force is \( 13 \, \text{N} \).