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The torque of a force \mathrm{}5 i+3 \hat{j}-7 \hat{k} about the origin is \mathrm{\tau}. If the force acts on a particle whose position vector is \mathrm{}2 \hat{i}+2 \hat{j}+\hat{k}, then the value of \mathrm{\tau} will be
 

Option: 1

11 \hat{i}+19 \hat{j}-4 \hat{k}
 


Option: 2

-11 \hat{i}+9 \hat{j}-16 \hat{k}


Option: 3

-17 \hat{i}+19 \hat{j}-4 \hat{k}


Option: 4

17 \hat{i}+9 \hat{j}+16 \hat{k}


Answers (1)

best_answer

 \begin{aligned} \vec{\mathrm{F}} & =5 \hat{\mathrm{i}}+3 \hat{\jmath}-7 \hat{\mathrm{k}} \\ & \vec{r}=2 \hat{\mathrm{i}}+2 \hat{\jmath}+\hat{\mathrm{k}} \\ & \vec{\tau}=\vec{\mathrm{r}} \times \vec{\mathrm{F}} \\ & =(2 \hat{\mathrm{i}}+2 \hat{\jmath}+\hat{\mathrm{k}}) \times(5 \hat{\mathrm{i}}+3 \hat{\jmath}-7 \hat{\mathrm{k}}) \\ & =(6 \hat{\mathrm{k}}+14 \hat{\jmath}-10 \hat{\mathrm{k}}-14 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}-3 \hat{\mathrm{i}}) \\ \vec{\tau} & =(-17 \hat{\mathrm{i}}+19 \hat{\jmath}-4 \hat{\mathrm{k}}) \end{aligned}

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jitender.kumar

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