A body constrained to move in y direction is subjected to a force given by `vec(F)=(-2hat(i)+15hat(j)+6hat(k))` N . What is the work done by this force in moving the body through a distance of `10 m` along y-axis ?

Explanation

To solve the problem, we need to calculate the work done by the force vector when the body moves through a distance of 10 meters along the y-axis. The work done by a force is given by the dot product of the force vector and the displacement vector.

### Step-by-Step Solution:

1. **Identify the Force Vector**:
The force vector is given as:
\[ \vec{F} = -2\hat{i} + 15\hat{j} + 6\hat{k} \text{ N} \]

2. **Identify the Displacement Vector**:
Since the body is constrained to move only in the y-direction and moves a distance of 10 m, the displacement vector is:
\[ \vec{S} = 10\hat{j} \text{ m} \]

3. **Calculate the Work Done**:
The work done \( W \) by the force is calculated using the dot product of the force vector and the displacement vector:
\[ W = \vec{F} \cdot \vec{S} \]
Substituting the values:
\[ W = (-2\hat{i} + 15\hat{j} + 6\hat{k}) \cdot (0\hat{i} + 10\hat{j} + 0\hat{k}) \]

4. **Perform the Dot Product**:
The dot product is calculated as follows:
\[ W = (-2 \cdot 0) + (15 \cdot 10) + (6 \cdot 0) = 0 + 150 + 0 = 150 \text{ J} \]

5. **Conclusion**:
Therefore, the work done by the force in moving the body through a distance of 10 m along the y-axis is:
\[ W = 150 \text{ J} \]