Vector sum of two forces of 10N and 6N cannot be:

Options

A. 4N
B. 8N
C. 12N
D. 2N

Answer

To solve the question regarding the vector sum of two forces of 10N and 6N, we need to determine the possible range of the resultant force. Here’s a step-by-step solution:

### Step 1: Identify the Forces
We have two forces:
- \( F_1 = 10 \, \text{N} \)
- \( F_2 = 6 \, \text{N} \)

### Step 2: Understand the Resultant Force
The resultant force \( F_r \) when adding two vectors can vary depending on the angle between them. The magnitude of the resultant force can be calculated using the following two conditions:
1. The maximum resultant force occurs when the two forces are in the same direction.
2. The minimum resultant force occurs when the two forces are in opposite directions.

### Step 3: Calculate Maximum Resultant Force
The maximum resultant force \( F_{r_{max}} \) is given by:
\[ F_{r_{max}} = F_1 + F_2 = 10 \, \text{N} + 6 \, \text{N} = 16 \, \text{N} \]

### Step 4: Calculate Minimum Resultant Force
The minimum resultant force \( F_{r_{min}} \) is given by:
\[ F_{r_{min}} = |F_1 - F_2| = |10 \, \text{N} - 6 \, \text{N}| = 4 \, \text{N} \]

### Step 5: Determine the Range of Resultant Force
The resultant force can therefore vary from:
\[ 4 \, \text{N} \quad \text{to} \quad 16 \, \text{N} \]

### Step 6: Check the Given Options
Now, we need to check which of the provided options falls outside this range. The possible resultant magnitudes must be between 4N and 16N, inclusive.

### Step 7: Identify the Incorrect Option
- If the options are:
- 4 N (valid)
- 8 N (valid)
- 12 N (valid)
- 2 N (not valid)

Since 2 N is less than the minimum resultant force of 4 N, it cannot be the vector sum of the two forces.

### Conclusion
The vector sum of the two forces of 10N and 6N cannot be **2 N**.

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