The gravitational field in a region is given by `vec(E) = (5hat(i) + 12 hat(j))N//Kg`. The change in gravitational potential energy if a particle of mass 1 kg is taken from the origin to the point (12m, 5m).

Explanation

To find the change in gravitational potential energy when a particle of mass 1 kg is moved from the origin (0, 0) to the point (12 m, 5 m) in a gravitational field given by \(\vec{E} = (5 \hat{i} + 12 \hat{j}) \, \text{N/kg}\), we can follow these steps:

### Step 1: Understand the formula for change in gravitational potential energy
The change in gravitational potential energy (\(\Delta U\)) when moving through a gravitational field can be calculated using the formula:
\[ \Delta U = -m \int_{\vec{r_1}}^{\vec{r_2}} \vec{E} \cdot d\vec{r} \]
where:
...