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

$\left(\frac{16}{5}, \frac{7}{5}, \frac{14}{5}\right)$

The correct answer is Option (2) → $\left(\frac{16}{5}, \frac{7}{5}, \frac{14}{5}\right)$

$\left(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n},\frac{mz_2+nz_1}{m+n}\right)$

Here,

$m=3$ and $n=2$

$P=(2,-1,4);Q=(4,3,2)$

$∴x=\frac{3.4+2.2}{3+2}=\frac{16}{5}$

$y=\frac{3.3+2.(-1)}{3+2}=\frac{7}{5}$

$z=\frac{3.2+2.4}{3+2}=\frac{14}{5}$