Question Number 43613 by indalecioneves last updated on 12/Sep/18
$${Be}\:{the}\:{vectors}\:\overset{\rightarrow} {{a}}\:=\:\left(\mathrm{1},\:−\mathrm{1},\:\mathrm{2}\right),\:\overset{\rightarrow} {{b}}\:=\:\left(−\mathrm{5},\:\:{k},\:{k}\right)\:{and}\:\overset{\rightarrow} {{c}}\:=\:\left(\mathrm{3},\:\mathrm{1},\:\mathrm{2}\right)\:{in}\:{the} \\ $$$${rectangular}\:{Cartesian}\:{coordinate}\:{system}.\:{For}\:{any}\:{vector}\:\overset{\rightarrow} {{r}},\:{the}\:{equation}\:\overset{\rightarrow} {{r}}×\overset{\rightarrow} {{a}}\:+\:{k}\overset{\rightarrow} {{b}}\:=\:\overset{\rightarrow} {{c}}\:{has}\:{a}\:{solution}\:{when}\:{k}\:{is}\:{equal}\:{to}? \\ $$