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` .
A. 5
B. 7
C. 8
D. 10

Answer 1

Correct Answer - D
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)`
`rArr (x+1)/(3) =(y-3)/(1)=(z-2)/(4)`
If the point C (5,5, `lambda`) line on AB, we have
`(5+1)/(3)=(5-3)/(1)=(lambda -2)/(4) rArr (lambda-2)/(4)=2 rArr lambda= (8+2) =10`