Question Number 64348 by Rio Michael last updated on 16/Jul/19
$${the}\:{vectors}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}\:{are}\:{such}\:{that}\:\mid\boldsymbol{{a}}\mid\:=\mathrm{3}\:,\:\mid\boldsymbol{{b}}\mid=\mathrm{5}\:{and}\:\boldsymbol{{a}}.\boldsymbol{{b}}=−\mathrm{14} \\ $$$${find}\:\mid\boldsymbol{{a}}−\boldsymbol{{b}}\mid \\ $$
Answered by Tanmay chaudhury last updated on 17/Jul/19
$$\mid\boldsymbol{{a}}−\boldsymbol{{b}}\mid^{\mathrm{2}} =\left(\boldsymbol{{a}}−\boldsymbol{{b}}\right).\left(\boldsymbol{{a}}−\boldsymbol{{b}}\right) \\ $$$$=\boldsymbol{{a}}.\boldsymbol{{a}}−\mathrm{2}\boldsymbol{{a}}.\boldsymbol{{b}}+\boldsymbol{{b}}.\boldsymbol{{b}} \\ $$$$=\mid\boldsymbol{{a}}\mid^{\mathrm{2}} −\mathrm{2}\boldsymbol{{a}}.\boldsymbol{{b}}+\mid\boldsymbol{{b}}\mid^{\mathrm{2}} \\ $$$$=\mathrm{9}+\mathrm{28}+\mathrm{25} \\ $$$$\mid\boldsymbol{{a}}−\boldsymbol{{b}}\mid=\sqrt{\mathrm{62}}\: \\ $$