Question

The ratio in which ZX-plane divides the line segment AB joining the points $A(4,2,3)$ and $B(-2,4,5)$ is equal to

• A. $1:2$ internally
• B. $1:2$ externally
• C. $-1:2$
• D. None of these

Answer 1

Answer: (B)

$1:2$ externally

Answer 2

Let $\lambda :1$ be the ratio in which ZX-plane divides the line segment AB. Day By section formula
$=\left( \frac{2\lambda +4}{\lambda +1},\frac{4\lambda +2}{\lambda +1},\frac{5\lambda +3}{\lambda +1} \right)$
For ZX-plane Cording of $y=0$
$\frac{4\lambda +2}{\lambda +1}=0$
$\Rightarrow$ $\lambda =-1/2$
$\Rightarrow$ $\lambda :1=-1:2$
Hence, ZX-plane i.e., point P divides the line segment AB in the ratio $1:2$ externally.