Question

Find the ratio in which the line joining the points $(2,4,5),(3,5,-4)$ is divided by the $yz$- plane

Answer 1

Let the point $P$ be the point on the YZ plane that divides the line joining those two poins.
Let the ratio of division by $1:\lambda$
Since $P$ lies on the YZ plane, the x-coordinate of $P$ is $0$.
Using the section formula gives us:
$0=\frac{2\lambda +3}{1+\lambda }⟹\lambda =-\frac{3}{2}$
A negative value of $\lambda$ denotes that the YZ plane is externally dividing the line and the ratio is $2:3$.