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A particle moves from $(1,0,3)$ to the point $(-3,4,5)$, when a force $\mathbf{F}=\hat{\mathbf{i}}+5 \hat{\mathbf{k}}$ acts on it. Amount of work done in joules is
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Verified Answer
The correct answer is:
6
Starting point of particle $=\hat{i}+3 \hat{k}$
$$
\begin{aligned}
\text { Ending point of particle } & =-3 \hat{i}+4 \hat{j}+5 \hat{k} \\
\text { force }(F) & =\hat{i}+5 \hat{k}
\end{aligned}
$$
$\therefore$ Displacement of the particle
$$
\begin{aligned}
(\mathbf{s}) & =(-3 \hat{i}+4 \hat{j}+5 \hat{k})-(\hat{i}+3 \hat{k}) \\
& =-4 \hat{i}+4 \hat{j}+2 \hat{k}
\end{aligned}
$$
We know that,
Work done, $W=\mathrm{F} \cdot \mathbf{s}$
or,
$$
\begin{aligned}
& W=(\hat{i}+5 \hat{k}) \cdot(-4 \hat{i}+4 \hat{j}+2 \hat{k}) \\
& W=-4+10 \text { or, } W=6 \mathrm{~J}
\end{aligned}
$$
$$
\begin{aligned}
\text { Ending point of particle } & =-3 \hat{i}+4 \hat{j}+5 \hat{k} \\
\text { force }(F) & =\hat{i}+5 \hat{k}
\end{aligned}
$$
$\therefore$ Displacement of the particle
$$
\begin{aligned}
(\mathbf{s}) & =(-3 \hat{i}+4 \hat{j}+5 \hat{k})-(\hat{i}+3 \hat{k}) \\
& =-4 \hat{i}+4 \hat{j}+2 \hat{k}
\end{aligned}
$$
We know that,
Work done, $W=\mathrm{F} \cdot \mathbf{s}$
or,
$$
\begin{aligned}
& W=(\hat{i}+5 \hat{k}) \cdot(-4 \hat{i}+4 \hat{j}+2 \hat{k}) \\
& W=-4+10 \text { or, } W=6 \mathrm{~J}
\end{aligned}
$$
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