Mathematics - Vector Question with Solution | TestHub

Work done by the forces ${\vec{F}}_1$ and ${\vec{F}}_2$ is $\left({\vec{F}}_1+{\vec{F}}_2\right)\cdot \vec{d}$, where $\vec{d}$ is displacement According to question ${\vec{F}}_1+{\vec{F}}_2=(4\hat{i}+\hat{j}-3\hat{k})+(3\hat{i}+\hat{j}-\hat{k})=7\hat{i}+2\hat{j}-4\hat{k}$ and $\vec{d}=(5\hat{i}+4\hat{j}+\hat{k})-(\hat{i}+2\hat{j}+3\hat{k})=4\hat{i}+2\hat{j}-2\hat{k}$. Hence $\left({\vec{F}}_1+{\vec{F}}_2\right)\cdot \vec{d}$ is 40