Question

If the points $A(3,-2,4)$, $B(1,1,1)$ and $C(-1,4,-2)$ are collinear, then the ratio in which $C$ divides $AB$ is

• A. $1:2$
• B. $-2:1$
• C. $-1:2$
• D. $4:0$

Answer 1

The correct option is B $-2:1$

Let $C$ divide $AB$ in the ratio $x:y$.
Let us compare the $x$-coordinate of $C$ by using section formula:
$-1=\frac{x\times 1+y\times 3}{x+y}$
$\Rightarrow x+3y=-x-y$
$\Rightarrow x=-2y$
Hence, point $C$ divides $AB$ in the ratio $-2:1$. As the ratio is negative, it means $C$ divides $AB$ externally