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 act at a point in mutually perpendicular directions, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Identify the Forces
We have three forces acting at a point:
- Force A = 3 N
- Force B = 4 N
- Force C = 12 N

### Step 2: Apply the Pythagorean Theorem
Since the forces are acting in mutually perpendicular directions, we can find the magnitude of the resultant force (R) using the formula:
\[ R = \sqrt{A^2 + B^2 + C^2} \]

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

### Step 4: Calculate Each Term
Calculate the squares of each force:
- \( (3 \, \text{N})^2 = 9 \, \text{N}^2 \)
- \( (4 \, \text{N})^2 = 16 \, \text{N}^2 \)
- \( (12 \, \text{N})^2 = 144 \, \text{N}^2 \)

### Step 5: Sum the Squares
Now, sum these squared values:
\[ 9 \, \text{N}^2 + 16 \, \text{N}^2 + 144 \, \text{N}^2 = 169 \, \text{N}^2 \]

### Step 6: Take the Square Root
Finally, take the square root to find the magnitude of the resultant force:
\[ R = \sqrt{169 \, \text{N}^2} = 13 \, \text{N} \]

### Conclusion
The magnitude of the resultant force is **13 N**.

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