Two constant force $\overrightarrow F_1 and \overrightarrow F_2$ acts on a body.these forces displaces the body from point P(1, -2, 3) to Q (2, 3, 7 ) in 2s starting from rest.force $\overrightarrow F_1$ is of magnitude 9 N and acting along vector $( 2 \hat i - 2 \hat j + \hat k )$ . the positions are in meter. find work done by $\overrightarrow F_1$.

$\begin{aligned}\vec{F}_{1}&=k(2\hat{i}-2\hat{\jmath}+\hat{k}) \\\vec{d}=&(2-1) \hat{1}+(3-(-2))\hat{j}\\&+(7-3) \hat{k} \\=&(1) \hat{1}+(5)\hat{j}+(4)\hat{k}\\\vec{W}_{1}=&\vec{F}_{1}\cdot\vec{d}\\&=k(2\hat{i}-2\hat{j}+\hat{k})\cdot(i+5\hat{j}+4\hat{k})......(i)\end{aligned}$

$|\vec{F}_1|=9$

$9=\sqrt{4 k^{2}+4 k^{2}+k^{2}}$

$9=3 k$

$k=3...(ii)$

$\text{putting (ii) in (i) we get}$

$\overrightarrow{W_{1}}=-12 \mathrm{~J}$