Question

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

Answer 1

The equations of the line AB are
`(x+1)/(-4+1) =(y-3)/(2-3) =(z-2)/(-2-2)`
`rArr (x+1)/(-3) =(y-3)/(-1) =(z-2)/(-4)`
Since the points A ,B and C are collinear so the point `C(5,5,lambda)` lies on (i)
`:. (5+1)/(-3) =(5-3)/(-1) =(lambda-2)/(-4) rArr (lambda-2)/(-4) =-2 rArr lambda-2 =8 rArr lambda =10`
Hence the required value of `lambda ` is 10.