A force `vec(F) = (2hat(i) - 3hat(j) +7hat(k))` N is applied on a particle which displaces it by `vec(S) = (4hat(i)+5hat(j) +hat(k))` . Find the work done on the particle .

Explanation

To find the work done on a particle when a force is applied to it and it displaces, 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} = 2\hat{i} - 3\hat{j} + 7\hat{k} \, \text{N}
...