To get a resultant displacement of 10 m, two displacement vectors, one of magnitude 6 m another of 8 m should be combined :

Options

A. parallel
B. anti-parallel
C. at an angle of
D. perpendicular to each other

Explanation

To solve the problem of finding the correct configuration of two displacement vectors (6 m and 8 m) that results in a resultant displacement of 10 m, we will analyze each option step by step.

### Step 1: Understand the vectors
We have two displacement vectors:
- \( \vec{F_1} \) with a magnitude of 6 m
- \( \vec{F_2} \) with a magnitude of 8 m

### Step 2: Check the first option - Parallel
If the two vectors are parallel, the resultant displacement \( R \) is given by:
\[ R = F_1 + F_2 = 6 \, \text{m} + 8 \, \text{m} = 14 \, \text{m} \]
Since we need a resultant of 10 m, this option is not valid.

### Step 3: Check the second option - Anti-parallel
If the two vectors are anti-parallel, the resultant displacement \( R \) is given by:
\[ R = F_2 - F_1 = 8 \, \text{m} - 6 \, \text{m} = 2 \, \text{m} \]
Again, since we need a resultant of 10 m, this option is also not valid.

### Step 4: Check the third option - At an angle
If the two vectors are at an angle \( \theta \), the resultant displacement \( R \) can be calculated using the formula:
\[ R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos(\theta)} \]
However, we will analyze the fourth option before making a conclusion.

### Step 5: Check the fourth option - Perpendicular
If the two vectors are perpendicular to each other, the resultant displacement \( R \) is given by:
\[ R = \sqrt{F_1^2 + F_2^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \, \text{m} \]
This matches our requirement of a resultant displacement of 10 m.

### Conclusion
The correct configuration of the two displacement vectors (6 m and 8 m) that results in a resultant displacement of 10 m is when they are **perpendicular** to each other.