A body of mass $4 \mathrm{~kg}$ experiences two forces $\vec{F}_1=5 \hat{i}+8 \hat{j}+7 \hat{k}$ and $\overrightarrow{\mathrm{F}}_2=3 \hat{i}-4 \hat{j}-3 \hat{k}$. The acceleration acting on the body is :

<p>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&#39;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 :</p> <p>$\vec{F} = m \cdot \vec{a}$</p> <p>or</p> <p>$\vec{a} = \frac{\vec{F}}{m}$</p> <p>Let&#39;s start by adding the forces:</p> <p>$$ \vec{F}_1 + \vec{F}_2 = (5 \hat{i}+8 \hat{j}+7 \hat{k}) + (3 \hat{i}-4 \hat{j}-3 \hat{k}) $$</p> <p>Performing the addition component-wise:</p> <p>$$ \vec{F}_{\text{total}} = (5 + 3)\hat{i} + (8 - 4)\hat{j} + (7 - 3)\hat{k} \ \vec{F}_{\text{total}} = 8 \hat{i} + 4 \hat{j} + 4 \hat{k} $$</p> <p>Now, let&#39;s use the formula for acceleration with $m = 4 \mathrm{~kg}$:</p> <p>$$ \vec{a} = \frac{\vec{F}_{\text{total}}}{m} = \frac{8 \hat{i} + 4 \hat{j} + 4 \hat{k}}{4 \mathrm{~kg}} $$</p> <p>Divide each component by the mass:</p> <p>$\vec{a} = 2 \hat{i} + 1 \hat{j} + 1 \hat{k}$</p> <p>So, the acceleration acting on the body is:</p> <p>$\vec{a} = 2 \hat{i} + \hat{j} + \hat{k}$</p> <p>Thus, the correct option is:</p> <p>Option A : <br/><br/>$2 \hat{i}+\hat{j}+\hat{k}$</p>