A force `vecF=5hati+6hatj+4hatk` acting on a body, produces a displacement `vecS=6hati-5hatk`. Work done by the force is

Options

A. 10 units
B. 18 units
C. 11 units
D. 5 units

Answer

To calculate the work done by the force on the body, we can use the formula for work done, which is given by the dot product of the force vector and the displacement vector.

### Step-by-Step Solution:

1. **Identify the Force and Displacement Vectors:**
The force vector is given as:
\[ \vec{F} = 5\hat{i} + 6\hat{j} + 4\hat{k} \]
The displacement vector is given as:
\[ \vec{S} = 6\hat{i} - 5\hat{k} \]

2. **Calculate the Dot Product:**
The work done \( W \) is calculated using the dot product of the force vector and the displacement vector:
\[ W = \vec{F} \cdot \vec{S} \]
The dot product is calculated as follows:
\[ \vec{F} \cdot \vec{S} = (5\hat{i} + 6\hat{j} + 4\hat{k}) \cdot (6\hat{i} + 0\hat{j} - 5\hat{k}) \]
This expands to:
\[ W = (5 \cdot 6) + (6 \cdot 0) + (4 \cdot -5) \]

3. **Perform the Multiplications:**
Calculate each term:
- \( 5 \cdot 6 = 30 \)
- \( 6 \cdot 0 = 0 \)
- \( 4 \cdot -5 = -20 \)

4. **Sum the Results:**
Now, add these results together:
\[ W = 30 + 0 - 20 = 10 \]

5. **Final Result:**
Therefore, the work done by the force is:
\[ W = 10 \text{ joules} \]

### Conclusion:
The work done by the force is **10 joules**.