Question

The x-y plane divides the line joining the points $(-1,3,4)$ and $(2,-5,6)$:

• A. internally in the ratio $2:3$
• B. externally in the ratio $2:3$
• C. internally in the ratio $3:2$
• D. externally in the ratio $3:2$

Answer 1

The correct option is A internally in the ratio $2:3$

Let $xy$ plane divides the line joining the points $A\left(-1,3,4\right)$ and $B\left(2,-5,6\right)$ in the ratio $k:1$.

$x=\frac{2k-1}{k+1}$

$y=\frac{-5k+3}{k+1}$

$z=\frac{6k-4}{k+1}$

Since the plane is $xy$ plane, so $z=0$,

$\frac{6k-4}{k+1}=0$

$6k-4=0$

$6k=4$

$k=\frac{4}{6}$

$k=\frac{2}{3}$

Therefore, the ratio is $2:3$ internally.