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

Given points are `:A(5,5,lamda),B(-1,3,2)andC(-4,2,-2)`
`:.` Direction ratios of line AB are
`-1,-5,3-5,2-lamdai.e.,-6,-2,2-lamda`
Direction ratios of line AC are
`-4,-5,2-5,-2-lamdai.e.,-9,-3,-2-lamda`
`:'` A, B, C are collinear.
`:.` Direction ratios are proportional.
`implies(-6)/(-9)=(-2)/(-3)=(2-lamda)/(-2-lamda)`
`implies(2-lamda)/(-2-lamda)=(2)/(3)`