Question

What is the ratio in which the line segment joining the points $(-3$ , $2$ , $5)$ and $(6$ , $3$ , $2)$ is divided by the $XY$ - plane?

• A. $2:5$ externally
• B. $5:2$ externally
• C. $3:5$ internally
• D. $5:2$ internally

Answer 1

Answer: (B)

Let $P$ divides the line segment joining the points $(-3,2,5)$ and $(6,3,2)$ in the ratio $k:1$.
So, coordinates of $P$ are $\left(\frac{6k-3}{k+1},\frac{3k+2}{k+1},\frac{2k+5}{k+1}\right)$.
Now, $P$ lies on plane $z=0$.
$[\because$ Equation of $XY$ plane is $Z=0$]
$\therefore \frac{2k+5}{k+1}=0$
$\Rightarrow k=-\frac{5}{2}$ or $5:2$ externally.