The ratio in which the plane `2x-1=0` divides the line joining `(-2,4,7)` and `(3,-5,8)` is

Options

A. `2:3`
B. `4:5`
C. `7:8`
D. `1:1`

Answer

D

Explanation

Let the required ratio be `k:1`. Then the coordinates of the point which divides the line joining the points `(-2,4,7)` and `(3,-5,8)` in the ratio are givn by `((3k-2)/(k+1), (-5k+4)/(k+1), (8k+7)/(k+1))`
As this point lies on the plane `2x-1=0`, we have
`(3k-1)/(k+1) = 1/2 rArr 1`
and thus the required ratios as `1:1`