The coordinates of a point dividing the line segment joining (3, 4, 5) and (1, 3, 6) externally in the ratio 3 : 1 are:

Correct option is D

​$$\begin{aligned}&\text{When a point } P \text{ divides the line segment joining } A(x_1, y_1, z_1) \text{ and } B(x_2, y_2, z_2) \text{ externally in the ratio } m:n, \text{ the coordinates of } P \text{ are given by:} \\\\&\qquad P\left(\frac{mx_2 - nx_1}{m - n}, \frac{my_2 - ny_1}{m - n}, \frac{mz_2 - nz_1}{m - n}\right) \\\\&\text{Here, } m = 3 \text{ and } n = 1. \\\\&\textbf{Apply the Formula} \\\\&\text{Given:} \\&\qquad \bullet \ A(3, 4, 5) \rightarrow (x_1, y_1, z_1) \\&\qquad \bullet \ B(1, 3, 6) \rightarrow (x_2, y_2, z_2) \\&\qquad \bullet \ \text{Ratio } 3:1 \rightarrow m = 3, n = 1 \\\\&\text{Now, compute the coordinates of } P: \\\\&\qquad x = \frac{mx_2 - nx_1}{m - n} = \frac{3 \times 1 - 1 \times 3}{3 - 1} = \frac{3 - 3}{2} = \frac{0}{2} = 0 \\\\&\qquad y = \frac{my_2 - ny_1}{m - n} = \frac{3 \times 3 - 1 \times 4}{3 - 1} = \frac{9 - 4}{2} = \frac{5}{2} \\\\&\qquad z = \frac{mz_2 - nz_1}{m - n} = \frac{3 \times 6 - 1 \times 5}{3 - 1} = \frac{18 - 5}{2} = \frac{13}{2} \\\\&\textbf{Final Answer} \\\\&\text{The coordinates of the point are:} \\\\&\qquad {\left(0, \frac{5}{2}, \frac{13}{2}\right)}\end{aligned}$$​​