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Q)

If $P(3,2,-4),\:Q(5,4,-6)\:and\:R(9,8,-10)$ are collinear,then $R$ divides $PQ$ in ratio?

$(a)\:3:2\:\:internally\:\:\qquad\:(b)\:3:2\:externally\:\:\qquad\:(c)\:2:1\:internally\:\:\qquad\:(d)\:2:1\:externally$.

Let the ratio be $\lambda:1$
According to section formula, the coordinates of R is given by $(\large\frac{5\lambda+3}{\lambda+1},\frac{4\lambda+2}{\lambda+1},\frac{-6\lambda-4}{\lambda+1})$
$\Rightarrow\:\large\frac{5\lambda+3}{\lambda+1}$$=9$
$\Rightarrow\:\lambda=-\large\frac{3}{2}$
$\therefore$ $R$ divides $PQ$ in ratio $3:2\:externally$ (since $\lambda$ is negative.)