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If A(3,2,-4),B(5,4,-6)a n dC(9,8,-10) ar...

If `A(3,2,-4),B(5,4,-6)a n dC(9,8,-10)` are three collinear points, then find the ratio in which point `C` divides `A Bdot`

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Let C divides AB in the ratio `lamda:1`. Then
`" "C-=((5lamda+3)/(lamda+1),(4lamda+2)/(lamda+1), (-6lamda-4)/(lamda+1))=(9, 8, -10)`
Comparing, we get
`" "5lamda+3=9lamda+9 or 4lamda=-6 or lamda=-3//2`
Also, from `4lamda+2=8lamda+8 and -6lamda-4=-10lamda-10`, we get the same value of `lamda`.
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