Let the ratio in which the point Q divides the line segment joining the

points P(3,2,-4) and R(9,8,-10) be k:1.

Using section formula,

\((5,4,-6)= (\dfrac{k(9)+3}{k+1}, \dfrac{k(8)+2}{k+1}, \)

\( \dfrac{k(-10)-4}{k+1} )\)

= \( \dfrac{9k+3}{k+1}=5\)

= 9k+3 = 5k+5

= 4k = 2

= \( k=\dfrac{2}{4}\)

k = \( \dfrac{1}{2}\)

Therefore, the ratio in which the point Q divides the line segment joining the points P(3,2,-4) and R(9,8,-10) is 1:2.

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