Question

If the points $A(2,1,1),B(0,-1,4)$ and $C(k,3,-2)$ are collinear, then $k=$ _____

• A. $0$
• B. $1$
• C. $4$
• D. $-4$

Answer 1

The correct option is C $4$

Equation of line passing through two points is given by,

$\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1}=\frac{z-z_1}{z_2-z_1}$

$\Rightarrow \frac{x-2}{2}=\frac{y-1}{2}=\frac{z-1}{-3}$

Now it is given above line passes through $(k,3,-2)$

So, $\frac{k-2}{2}=\frac{3-1}{2}=\frac{-2-1}{-3}$

$\Rightarrow \frac{k-2}{2}=1\Rightarrow k-2=2$

$\therefore k=4$