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Question-55913




Question Number 55913 by peter frank last updated on 06/Mar/19
Answered by tanmay.chaudhury50@gmail.com last updated on 06/Mar/19
OA^→ =−2i+2j+3k  OB^→ =2i−3j+k  OC^→ =4i+5j+3k  BC^→ =OC^→ −OB^→ =2i+8j+2k  in question no value of force also direction  not given.  assuming magnetude of force  F and direction OA^→   mid point of B and C is D(3,1,2)   OD^→ =3i+j+2k  BD^→ =OD^→ −OB^→   BD^→ =i+4j+k  DC^→ =OC^→ −OD^→   DC^→ =i+4j+k  workdone  B→D then D→C  F(−2i+2j+3k).(i+4j+k)+(F/2)(−2i+2j+3k).(i+4j+k)  ((3F)/2)(−2+8+3)  ((27F)/2)
$${O}\overset{\rightarrow} {{A}}=−\mathrm{2}{i}+\mathrm{2}{j}+\mathrm{3}{k} \\ $$$${O}\overset{\rightarrow} {{B}}=\mathrm{2}{i}−\mathrm{3}{j}+{k} \\ $$$${O}\overset{\rightarrow} {{C}}=\mathrm{4}{i}+\mathrm{5}{j}+\mathrm{3}{k} \\ $$$${B}\overset{\rightarrow} {{C}}={O}\overset{\rightarrow} {{C}}−{O}\overset{\rightarrow} {{B}}=\mathrm{2}{i}+\mathrm{8}{j}+\mathrm{2}{k} \\ $$$${in}\:{question}\:{no}\:{value}\:{of}\:{force}\:{also}\:{direction} \\ $$$${not}\:{given}.\:\:{assuming}\:{magnetude}\:{of}\:{force} \\ $$$${F}\:{and}\:{direction}\:{O}\overset{\rightarrow} {{A}} \\ $$$${mid}\:{point}\:{of}\:{B}\:{and}\:{C}\:{is}\:{D}\left(\mathrm{3},\mathrm{1},\mathrm{2}\right)\: \\ $$$${O}\overset{\rightarrow} {{D}}=\mathrm{3}{i}+{j}+\mathrm{2}{k} \\ $$$${B}\overset{\rightarrow} {{D}}={O}\overset{\rightarrow} {{D}}−{O}\overset{\rightarrow} {{B}} \\ $$$${B}\overset{\rightarrow} {{D}}={i}+\mathrm{4}{j}+{k} \\ $$$${D}\overset{\rightarrow} {{C}}={O}\overset{\rightarrow} {{C}}−{O}\overset{\rightarrow} {{D}} \\ $$$${D}\overset{\rightarrow} {{C}}={i}+\mathrm{4}{j}+{k} \\ $$$${workdone} \\ $$$${B}\rightarrow{D}\:{then}\:{D}\rightarrow{C} \\ $$$${F}\left(−\mathrm{2}{i}+\mathrm{2}{j}+\mathrm{3}{k}\right).\left({i}+\mathrm{4}{j}+{k}\right)+\frac{{F}}{\mathrm{2}}\left(−\mathrm{2}{i}+\mathrm{2}{j}+\mathrm{3}{k}\right).\left({i}+\mathrm{4}{j}+{k}\right) \\ $$$$\frac{\mathrm{3}{F}}{\mathrm{2}}\left(−\mathrm{2}+\mathrm{8}+\mathrm{3}\right) \\ $$$$\frac{\mathrm{27}{F}}{\mathrm{2}} \\ $$$$ \\ $$

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