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

Options

A. 18 units
B. 15 units
C. 12 units
D. 10 units

Explanation

To find the work done by the force acting on the body, we will 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. **Apply the Work Done Formula**:
- The work done \( W \) is calculated using the dot product:
\[ W = \vec{F} \cdot \vec{s} \]

3. **Calculate the Dot Product**:
- The dot product of two vectors \( \vec{A} = a_1\hat{i} + a_2\hat{j} + a_3\hat{k} \) and \( \vec{B} = b_1\hat{i} + b_2\hat{j} + b_3\hat{k} \) is given by:
\[ \vec{A} \cdot \vec{B} = a_1b_1 + a_2b_2 + a_3b_3 \]
- For our vectors:
\[ \vec{F} \cdot \vec{s} = (5)(6) + (6)(0) + (-4)(5) \]
- Calculate each term:
- First term: \( 5 \times 6 = 30 \)
- Second term: \( 6 \times 0 = 0 \)
- Third term: \( -4 \times 5 = -20 \)

4. **Combine the Results**:
- Now, sum the results of the dot product:
\[ W = 30 + 0 - 20 = 10 \]

5. **Conclusion**:
- The work done by the force is:
\[ W = 10 \text{ units} \]

### Final Answer:
The work done by the force is **10 units**.