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The co-ordinates of the point which divides the join of the points $(2, - 1, 3)$ and $(4, 3, 1)$ in the ratio $3 : 4$ internally are given by

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$\frac{2}{7}, \frac{20}{7}, \frac{10}{7}$

$\frac{15}{7}, \frac{20}{7}, \frac{3}{7}$

$\frac{20}{7}, \frac{5}{7}, \frac{15}{7}$

$\frac{10}{7}, \frac{15}{7}, \frac{2}{7}$

answer is D.

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Detailed Solution

From $x = \frac{m_{1} x_{2} + m_{2} x_{1}}{m_{1} + m_{2}}, y = \frac{m_{1} y_{2} + m_{2} y_{1}}{m_{1} + m_{2}},$

$z = \frac{m_{1} z_{2} + m_{2} z_{1}}{m_{1} + m_{2}}; x = \frac{20}{7}, y = \frac{5}{7}, z = \frac{15}{7} .$

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