To find the acceleration acting on the body, we first need to determine the resultant force acting on the body by adding the two forces $\vec{F}_1$ and $\vec{F}_2$ vectorially. Then, we apply Newton's second law of motion, which states that the acceleration $\vec{a}$ of a body is directly proportional to the total force $\vec{F}$ acting on it and inversely proportional to the mass $m$ of the body :

$$ \vec{F} = m \cdot \vec{a} $$

or

$$ \vec{a} = \frac{\vec{F}}{m} $$

Let's start by adding the forces:

$$ \vec{F}_1 + \vec{F}_2 = (5 \hat{i}+8 \hat{j}+7 \hat{k}) + (3 \hat{i}-4 \hat{j}-3 \hat{k}) $$

Performing the addition component-wise:

$$ \vec{F}_{\text{total}} = (5 + 3)\hat{i} + (8 - 4)\hat{j} + (7 - 3)\hat{k} \ \vec{F}_{\text{total}} = 8 \hat{i} + 4 \hat{j} + 4 \hat{k} $$

Now, let's use the formula for acceleration with $m = 4 \mathrm{~kg}$:

$$ \vec{a} = \frac{\vec{F}_{\text{total}}}{m} = \frac{8 \hat{i} + 4 \hat{j} + 4 \hat{k}}{4 \mathrm{~kg}} $$

Divide each component by the mass:

$$ \vec{a} = 2 \hat{i} + 1 \hat{j} + 1 \hat{k} $$

So, the acceleration acting on the body is:

$$ \vec{a} = 2 \hat{i} + \hat{j} + \hat{k}$$

Thus, the correct option is:

Option A :

$$2 \hat{i}+\hat{j}+\hat{k}$$