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

Options

A. `2:3`
B. `3:2`
C. `-2:3`
D. `4:-3`

Answer

C

Explanation

Let the point `R` divides the line joining the points `P(2,4,5)` and `Q(3,5,-4)` in the ratio `m:n`. Then the coordinate of `R` is
`((3m+2n)/(m+n),(5m+4n)/(m+n),(-4m+5n)/(m+n))`
For yz- plane, x-coordinate will be zero.
`:.(3m+2n)/(m+n)=0`
`impliesm/n=(-2)/3`
Alternate solution
The ratio in which yz-plane divides the line segment `-x_(1):x_(2)=-2:3`.