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

Explanation

To solve the problem of determining the possible vector sum of two forces of 10N and 6N, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Vector Addition**:
- When adding two vectors, the magnitude of the resultant vector (R) can vary based on the angle between the two vectors. The resultant will always lie between the sum and the difference of the two magnitudes.

2. **Calculate the Maximum Resultant**:
- The maximum possible resultant occurs when the two vectors are in the same direction.
- Therefore, R_max = 10N + 6N = 16N.

3. **Calculate the Minimum Resultant**:
- The minimum possible resultant occurs when the two vectors are in opposite directions.
- Therefore, R_min = |10N - 6N| = 10N - 6N = 4N.

4. **Determine the Range of Possible Resultants**:
- Based on the above calculations, the magnitude of the resultant vector must lie between the minimum and maximum values:
- 4N < R < 16N.

5. **Identify Values that Cannot Be Resultants**:
- From the range determined, any resultant vector that is less than 4N or greater than 16N is not possible.
- Thus, the vector sum of 10N and 6N cannot be any value outside the range (4N, 16N).

### Conclusion:
The vector sum of two forces of 10N and 6N cannot be less than 4N or greater than 16N. Therefore, any value below 4N or above 16N is not possible.