Question Number 73222 by Tanmay chaudhury last updated on 08/Nov/19
Answered by Tanmay chaudhury last updated on 08/Nov/19
$$\left[\overset{\rightarrow} {{a}}\overset{\rightarrow} {{b}}\overset{\rightarrow} {{c}}\right]=\mathrm{2}=\left(\overset{\rightarrow} {{a}}×\overset{\rightarrow} {{b}}\right).\overset{\rightarrow} {{c}} \\ $$$${l}\left(\overset{\rightarrow} {{b}}×\overset{\rightarrow} {{c}}\right).\overset{\rightarrow} {{c}}+{m}\left(\overset{\rightarrow} {{c}}×\overset{\rightarrow} {{a}}\right).\overset{\rightarrow} {{c}}+{n}\left(\overset{\rightarrow} {{a}}×\overset{\rightarrow} {{b}}\right).\overset{\rightarrow} {{c}}=\mathrm{4}{i}.\overset{\rightarrow} {{c}} \\ $$$${l}×\mathrm{0}+{m}×\mathrm{0}+{n}\left[{abc}\right]=\mathrm{4}{i}.\left({ic}_{{x}} +{jc}_{{y}} +{kc}_{{z}} \right)=\mathrm{4}{c}_{{x}} \\ $$$$\mathrm{2}{n}=\mathrm{4}{c}_{{x}} \:{similarly}\:\mathrm{2}{l}=\mathrm{4}{a}_{{x}} \:\:\:\mathrm{2}{m}=\mathrm{4}{b}_{{x}} \\ $$$${i}\left({a}_{{x}} +{b}_{{x}} +{c}_{{x}} \right)=\mathrm{3}{i}\rightarrow{a}_{{x}} +{b}_{{x}} +{c}_{{x}} =\mathrm{3} \\ $$$$\mathrm{2}\left({l}+{m}+{n}\right)=\mathrm{4}\left({a}_{{x}} +{b}_{{x}} +{c}_{{x}} \right)=\mathrm{4}×\mathrm{3} \\ $$$${l}+{m}+{n}=\mathrm{6} \\ $$$${plz}\:{check} \\ $$