A particle acted on by constant forces $4 \hat{i}+\hat{j}-3 \hat{k}$ and $3 \hat{i}+\hat{j}-\hat{k}$ to the…
A particle acted on by constant forces $4 \hat{i}+\hat{j}-3 \hat{k}$ and $3 \hat{i}+\hat{j}-\hat{k}$ to the point $5 \hat{i}+4 \hat{j}-\hat{k}$. The total work done by the forces is
50 units
20 units
30 units
40 units
Solution
$\overrightarrow{\mathrm{F}}+\overrightarrow{\mathrm{F}}_1+\overrightarrow{\mathrm{F}}_2=7 \mathrm{i}+2 \mathrm{j}-4 \mathrm{k}$
$\overrightarrow{\mathrm{d}}=\mathrm{P} \cdot \mathrm{V}$ of $\overrightarrow{\mathrm{B}}-\mathrm{P} \cdot \mathrm{V}$ of $\overrightarrow{\mathrm{A}}=4 \mathrm{i}+2 \mathrm{j}-2 \mathrm{k}$
$\mathrm{W}=\overrightarrow{\mathrm{F}} \cdot \overrightarrow{\mathrm{d}}=28+4+8=40$ unit