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The ratio in which the plane 2x-1=0 divi...

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

A

`2:3`

B

`4:5`

C

`7:8`

D

`1:1`

Text Solution

Verified by Experts

The correct Answer is:
D
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`
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Knowledge Check

  • The ration in which the plane 4x+5y-3z=8 divides the line joining the point (-2,1,5) and (3 ,3, 2) is

    A
    `3:2`
    B
    `5:3`
    C
    `1:4`
    D
    `2:1`

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    A
    `-4:1`
    B
    `3:2`
    C
    `-2:3`
    D
    `1:4`

  • The ratio in which the point (5, 4) divides the line joining points (2, 1) and (7,6 ) is…..

    A
    `3 : 2`
    B
    `2 : 3`
    C
    `1 : 3`
    D
    `2 : 3`

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