Question

The ratio in which YZ-plane divides the line segment formed by joining the points $(-2,4,7)$ and $(3,-5,8)$, is

• A. 2 : 3 (externally)
• B. 2 : 3 (internally)
• C. 1 : 3 (externally)
• D. 1 : 3 (internally)

Answer 1

Answer: (B)

The given points are $A(-2,4,7)$ and $B(3,-5,8)$. Let the point $P(0,y,z)$ in YZ-plane divides $AB$ in the ratio k: 1. Then.

$x$ -coordinate of point $P=\frac{m{x}_2+n{x}_1}{m+n}$
$\frac{k\times 3+1\times (-2)}{k+1}=0$
($\because x$ -coordinate of $P$ is zero)
$\Rightarrow 3k-2=0$
$\Rightarrow k=\frac{2}{3}$
$\Rightarrow k:1=2:3$
$\therefore$ YZ-plane divides the segment internally in the ratio $2:3$