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Read the following passage and answer th...

Read the following passage and answer the questions. Consider the lines
`L_(1):(x+1)/(3)=(y+2)/(1)=(z+1)/(2),L_(2):(x-2)/(1)=(y+2)/(2)=(z-3)/(3)`
The distance of the point (1,1,1) from the plane passing throught the point (-1,-2,-1) and whose normal is perpendicular to both the lines `L_(1)` and `L_(2)`, is

A

`2//sqrt(75)` unit

B

`7//sqrt(75)` units

C

`13//sqrt(75)` units

D

`23//sqrt(75)` units

Text Solution

Verified by Experts

The correct Answer is:
C
The equation of the plane passing through the point (-1,-2,-1) and whose normal is perpendicular to both the given lines `L_(1)` and `L_(2)` may be written as
`(x+1)+7(y+2)-5(z+1)=0impliesx+7y-5z+10=0`
The distance of the point (1,1,1) from the plane
`=|(1+7-5+10)/(sqrt(1+49+25))|=(13)/(sqrt(75))`units
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