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 combining two displacement vectors of magnitudes 6 m and 8 m to achieve a resultant displacement of 10 m, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Let vector A = 6 m
- Let vector B = 8 m
- Resultant vector R = 10 m

2. **Use the Formula for Resultant of Two Vectors:**
The formula to find the resultant of two vectors A and B at an angle θ is given by:
\[ R = \sqrt{A^2 + B^2 + 2AB \cos(\theta)} \]

3. **Substitute the Known Values into the Formula:**
Substitute A, B, and R into the formula:
\[ 10 = \sqrt{6^2 + 8^2 + 2 \cdot 6 \cdot 8 \cdot \cos(\theta)} \]
This simplifies to:
\[ 10 = \sqrt{36 + 64 + 96 \cos(\theta)} \]

4. **Square Both Sides to Eliminate the Square Root:**
\[ 10^2 = 36 + 64 + 96 \cos(\theta) \]
\[ 100 = 100 + 96 \cos(\theta) \]

5. **Rearrange the Equation:**
Subtract 100 from both sides:
\[ 0 = 96 \cos(\theta) \]

6. **Solve for cos(θ):**
\[ \cos(\theta) = 0 \]

7. **Determine the Angle θ:**
The cosine of an angle is zero at:
\[ \theta = 90^\circ \]

8. **Conclusion:**
The two displacement vectors of 6 m and 8 m must be combined at an angle of 90 degrees to achieve a resultant displacement of 10 m.