Point C divides line joining A(1,2,3)m and B(2,4,-6)m in 2 : 1. If the position vector of point C is$r_c=\left(x\hat{i}+y\hat{j}+z\hat{k}\right)$ m. Find the value of $-\frac{zy}{x}$

$r_c=\frac{n{r}_A+m{r}_B}{m+n}$   or  $r_c=\frac{1\left(\hat{i}+2\hat{j}+3\hat{k}\right)+2\left(2\hat{i}+4\hat{j}-6\hat{k}\right)}{3}$ $=\frac{5\hat{i}+10\hat{j}-9\hat{k}}{3}=\frac{5}{3}\hat{i}+\frac{10}{3}\hat{j}-3\hat{k}$

$\therefore x=\frac{5}{3},y=\frac{10}{3},z=-3$         $\therefore -\frac{zy}{x}=-\frac{\left(-3\right)\left(10/3\right)}{5/3}=6$