Three forces are acting on a body to make it in equilibrium , which set can not do it ?

Options

A. 3N,3N,7N
B. 2N,3N,6N
C. 2N, 1N, 1N
D. 8N,6N,1N

Explanation

To determine which set of forces cannot keep a body in equilibrium, we can apply the triangle inequality theorem. The triangle inequality states that for any three sides of a triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the third side.

### Step-by-Step Solution:

1. **Understanding Equilibrium**:
For a body to be in equilibrium under the action of three forces \( F_1 \), \( F_2 \), and \( F_3 \), the vector sum of these forces must equal zero:
\[ F_1 + F_2 + F_3 = 0 \]

2. **Applying Triangle Inequality**:
According to the triangle inequality, for the forces to be in equilibrium, the following conditions must hold:
\[ |F_1| + |F_2| \geq |F_3| \]
\[ |F_1| + |F_3| \geq |F_2| \]
\[ |F_2| + |F_3| \geq |F_1| \]

3. **Evaluating Each Option**:
We will evaluate each option provided to see if they satisfy the triangle inequality.

- **Option A**: \( F_1 = 3 \), \( F_2 = 3 \), \( F_3 = 7 \)
- Check: \( 3 + 3 < 7 \) (Does not satisfy)

- **Option B**: \( F_1 = 2 \), \( F_2 = 3 \), \( F_3 = 6 \)
- Check: \( 2 + 3 < 6 \) (Does not satisfy)

- **Option C**: \( F_1 = 2 \), \( F_2 = 1 \), \( F_3 = 1 \)
- Check: \( 2 + 1 > 1 \), \( 1 + 1 = 2 \) (Satisfies)

- **Option D**: \( F_1 = 6 \), \( F_2 = 1 \), \( F_3 = 8 \)
- Check: \( 6 + 1 < 8 \) (Does not satisfy)

4. **Conclusion**:
The sets that cannot keep the body in equilibrium are:
- Option A: \( (3, 3, 7) \)
- Option B: \( (2, 3, 6) \)
- Option D: \( (6, 1, 8) \)

Thus, the correct answer is that options A, B, and D cannot keep the body in equilibrium.