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

Options

A. 12
B. 13
C. 7
D. 19

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 and Directions**:
- Let the forces act along the x-axis, y-axis, and z-axis respectively.
- Force along x-axis, \( F_x = 3 \, \text{N} \)
- Force along y-axis, \( F_y = 4 \, \text{N} \)
- Force along z-axis, \( F_z = 12 \, \text{N} \)

2. **Use the Formula for Resultant Force**:
- The magnitude of the resultant force \( R \) can be calculated using the formula:
\[ R = \sqrt{F_x^2 + F_y^2 + F_z^2} \]

3. **Substitute the Values**:
- Substitute the values of the forces into the formula:
\[ R = \sqrt{(3 \, \text{N})^2 + (4 \, \text{N})^2 + (12 \, \text{N})^2} \]

4. **Calculate Each Term**:
- Calculate \( (3 \, \text{N})^2 = 9 \)
- Calculate \( (4 \, \text{N})^2 = 16 \)
- Calculate \( (12 \, \text{N})^2 = 144 \)

5. **Sum the Squares**:
- Add the squared values:
\[ 9 + 16 + 144 = 169 \]

6. **Take the Square Root**:
- Now take the square root of the sum:
\[ R = \sqrt{169} = 13 \, \text{N} \]

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

### Final Answer:
The magnitude of the resultant force is **13 N**.