Question

If the points $a(1,2,-1),B(2,6,2)$ and $c(\lambda ,-2,-4)$ are collinear then $\lambda$ is

• A. $0$
• B. $2$
• C. $-2$
• D. $1$

Answer 1

The correct option is A $0$

D.R of AB are $2-1,6-2,2-(-1)i.e.1,4,3$

D.R. of AC are $\lambda .-1,-2-2,-4-(-1)$

$i.e.,\lambda -1,-4,-3$

Since A, B, C are collinear $\therefore AB||BC$

$\therefore \frac{\lambda -1}{1}=\frac{-4}{4}=\frac{-3}{3}$

$⟹\lambda -1=-1$

$\therefore \lambda =0$