If  $2\overline{a}+3\overline{b}+5\overline{c}=0$  then $(a\times b)+(b\times c)+(\overline{c}\times \overline{a})=k(\overline{c}\times \overline{a})$  then k =

  $2\overline{a}+3\overline{b}+5\overline{c}=\overline{0}\Rightarrow (2\overline{a}+3\overline{b}+5\overline{c})\times \overline{b}=\overline{0}\times \overline{b}$
 $2(\overline{a}\times \overline{b})+3(\overline{b}\times \overline{b})+5(\overline{c}\times \overline{b})=0$
 $2(\overline{a}\times \overline{b})=5(\overline{b}\times \overline{c})$
$\overline{a}\times \overline{b}=\frac{5}{2}(\overline{b}\times \overline{c})$ , similarly we can find $\overline{a}\times \overline{c}$  interms of  $\overline{b}\times \overline{c}$
 $\Rightarrow K=\frac{10}{3}$