Let P(2, -1, 4) and Q (4, 3, 2) are two points and a point R on PQ is such that 3 PQ = 5 QR, then the coordinates of R are

$\left(\frac{14}{5}, \frac{3}{5}, \frac{16}{5}\right)$

Clearly, R divided PQ internally in the ratio 2 : 3.

So, the coordinates of R are

$\left(\frac{2×4+3×2}{2+3},\frac{2×3+3×(-1)}{2+3},\frac{2×2+3×4}{2+3} \right)\, or \,\left(\frac{14}{5}, \frac{3}{5}, \frac{16}{5} \right)$