Find the value of `lambda`. If the points `A(-1,3,2), B(-4,2,-2)` and `C(5,lambda,10)` are collinear.

Options

A. `2`
B. `3`
C. `4`
D. `5`

Answer

D

Explanation

`(x+1)/(-4-(-1))= (y-3)/(2-3) = (z-2)/(2-2)`
`rArr (x+1)/(-3) = (y-3)/(-1) = (z-2)/(1)`
`rArr (x+1)/(3) = (y-3)/(1) = (z-2)/(4) "….."(1)`
`:. A, B` and C points are collinear.
`:.` Point C will lie on `(1)`
`(5+1)/(3) = (lambda - 3)/(1) = (10-2)/(4)`
`rArr 2 = lambda - 3 = 2`
`rArr lambda = 5`.