Given that `P(3,2,-4),Q(5,4,-6) and R(9,8,-10)` are collinear. Find the ratio in which `Q` divide `P Rdot`

Explanation

Let point `Q(5,4,-6) `divide the line segment joining points `P(3,2,-4)` and `R(9,8,- 10 )` in the ratio k: 1.

Therefore,

by section formula,


`(5,4,-6)=(frac{k(9)+3}{k+1}, frac{k(8)+2}{k+1}, frac{k(-10)-4}{k+1}) `
`
Rightarrow frac{9 k+3}{k+1}=5 `
`
Rightarrow 9 k+3=5 k+5 `
`
Rightarrow 4 k=2`
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