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