Question

If $A(1,2,1),B(2,6,2)$ and $C(\lambda ,14,4)$ are collinear, then value of $\lambda$ is

Answer 1

Equation of line $AB$ is given by,
$\frac{x-1}{1}=\frac{y-2}{4}=\frac{z-1}{1}$
For $A,B,C$ to be collinear, $C$ must also lie on the line $AB$,
$\Rightarrow \frac{\lambda -1}{1}=\frac{14-2}{4}=\frac{4-1}{1}$
$\Rightarrow \lambda -1=3$

$\Rightarrow \lambda =4$