Distance of point P(-2,3,4) from the lin...

Distance of point `P(-2,3,4)` from the line `(x+2)/3=(2y+3)/4=(3z+4)/5` measured parallel to the plane `8x+6y-9z+1=0` is

A

`(sqrt(301))/2`

B

`(sqrt(401))/2`

C

`(sqrt(307))/2`

D

`(sqrt(207))/2`

Text Solution

Verified by Experts

The correct Answer is:

B

`(x+2)/3=(y+3/2)/2=(z+4/3)/(5/3)=lamda`…………(1)
`P(-2,3,4)`
any variable point on line (1) `A(3lamda-2,2lamda-3/2, 5/3lamda-4/3)`
no line `AP` and normal of given plane are perpendicular
`implies (3lamda)8+((4lamda-9)/2)6+((5lamda-16)/3)(-9)=0`
`implieslamda=-1`
Distance `=sqrt(401)/2`

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