If the points `A(-1,3,2),B(-4,2,-2)a n dC(5,5,lambda)` are collinear, find the value of `lambda` .

Explanation

equations of the line A B are



`frac{x+1}{-4+1}=frac{y-3}{2-3}=frac{z-2}{-2-2} `


`Rightarrow frac{x+1}{-3}=frac{y-3}{-1}=frac{z-2}{-4}`



Here the points A, B and C are collinear so the point C(5,5, lambda) lies on (i)

`

therefore frac{5+1}{-3}=frac{5-3}{-1}=frac{lambda-2}{-4} Rightarrow frac{lambda-2}{-4}=-2 Rightarrow lambda-2=8 Rightarrow lambda=10`


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