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\(A\) force \(\mathbf{F}=(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N}\) acts on a body and produces a displacement \(s=(6 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \mathrm{m}\). The work done by the force is
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Verified Answer
The correct answer is:
\(10 \mathrm{~J}\)
Force applied on the body,
\(\begin{aligned}
\mathbf{F} & =(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N} \\
\text {Displacement, } \mathbf{s} & =(6 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \mathrm{m} \\
\therefore \text { Work done, } W & =\mathbf{F} \cdot \mathbf{s}=(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \cdot(6 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \\
& =30-20+0=10 \mathrm{~J}
\end{aligned}\)
\(\begin{aligned}
\mathbf{F} & =(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N} \\
\text {Displacement, } \mathbf{s} & =(6 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \mathrm{m} \\
\therefore \text { Work done, } W & =\mathbf{F} \cdot \mathbf{s}=(5 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \cdot(6 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \\
& =30-20+0=10 \mathrm{~J}
\end{aligned}\)
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