Question

If the points $(-1,2,1),(2,1,0),(\lambda ,3,2)$ are collinear, then which of the following can be correct ?

• A. $2{\lambda }^2-9\lambda +4=0$
• B. $2{\lambda }^2+7\lambda -4=0$
• C. ${\lambda }^2+\lambda -12=0$
• D. ${\lambda }^2-\lambda -12=0$

Answer 1

Answer: (B), (C)

${\lambda }^2+\lambda -12=0$

For collinear points:
$\frac{x_3-x_1}{x_2-x_1}=\frac{y_3-y_1}{y_2-y_1}=\frac{z_3-z_1}{z_2-z_1}$
$\Rightarrow \frac{\lambda +1}{2+1}=\frac{3-2}{1-2}=\frac{2-1}{0-1}$
$\Rightarrow \frac{\lambda +1}{3}=-1$
$\Rightarrow \lambda +1=-3$
$\Rightarrow \lambda =-4$