Question

Find the ratio in which the join of the points P(2, -1, 3) and Q(4, 3, 1) is divided by the point $(\frac{20}{7},\frac{5}{7},\frac{15}{7})$.

Answer 1

Let the required ratio be $\lambda :1$. Then, the coordinates of R are

$(\frac{4\lambda +2}{\lambda +1},\frac{3\lambda -1}{\lambda +1},\frac{\lambda +3}{\lambda +1})$.

But, the coordinates of R are $(\frac{20}{7},\frac{5}{7},\frac{15}{7})$

$\therefore \frac{4\lambda +2}{\lambda +1}=\frac{20}{7}$ or $\lambda =\frac{3}{4}$.

So, the required ratio is $\frac{3}{4}:1$, i.e., 3:4.