Two force vectors `vecF_1` and` vecF_2` , each of magnitude 10 N act at a point at an angle of 60°. The magnitude of resultant force vector is

Options

A. 10N
B. `10sqrt3` N
C. 20 N
D. `20sqrt3 N`

Answer

To find the magnitude of the resultant force vector when two force vectors \(\vec{F_1}\) and \(\vec{F_2}\) each of magnitude 10 N act at an angle of 60°, we can use the following steps:

### Step-by-Step Solution:

1. **Identify the Forces and Angle**:
- Given: Magnitude of \(\vec{F_1} = 10 \, \text{N}\)
- Given: Magnitude of \(\vec{F_2} = 10 \, \text{N}\)
- Angle between \(\vec{F_1}\) and \(\vec{F_2} = 60^\circ\)

2. **Use the Formula for Resultant of Two Vectors**:
The magnitude of the resultant force \(R\) when two forces are acting at an angle \(\theta\) is given by:
\[ R = \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos(\theta)} \]

3. **Substitute the Values**:
- Here, \(F_1 = 10 \, \text{N}\), \(F_2 = 10 \, \text{N}\), and \(\theta = 60^\circ\).
- Substitute these values into the formula:
\[ R = \sqrt{10^2 + 10^2 + 2 \cdot 10 \cdot 10 \cdot \cos(60^\circ)} \]

4. **Calculate \(\cos(60^\circ)\)**:
- We know that \(\cos(60^\circ) = \frac{1}{2}\).
- Substitute this into the equation:
\[ R = \sqrt{10^2 + 10^2 + 2 \cdot 10 \cdot 10 \cdot \frac{1}{2}} \]

5. **Simplify the Expression**:
- Calculate \(10^2 + 10^2 = 100 + 100 = 200\).
- Calculate \(2 \cdot 10 \cdot 10 \cdot \frac{1}{2} = 100\).
- Now, substitute these values back:
\[ R = \sqrt{200 + 100} = \sqrt{300} \]

6. **Final Calculation**:
- Simplify \(\sqrt{300}\):
\[ R = \sqrt{100 \cdot 3} = 10\sqrt{3} \, \text{N} \]

### Conclusion:
The magnitude of the resultant force vector is \(10\sqrt{3} \, \text{N}\).