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The equation of the plane passing throug...

The equation of the plane passing through the mid - point of the line joining the points (1,2,3) and (3,4,5) and perpendicular to it is

A

`x+y+z=9`

B

`x+y+z=-9`

C

`2x+3y+4z=9`

D

`2x+3y+4z=-9`

Text Solution

Verified by Experts

The correct Answer is:
A
The DR's of the joining the points (1,23 and (3,4,5) are (3-1,4-2,5-3) i.e. (2,2,2).
Also, the mid - point of the join of the points (1,2,3) and (3,4,5) is `((1+3)/(2),(4+2)/(2),(5+3)/(2))` i.e, (2,3,4).
`:.` Equation of plane which passes through (2,3,4) and Dr's of its normal are (2,2,2) is
`2(x-2)+2(y-3)+2(z-4)=0`
`rArr" "x+y+z-9=0`
`rArr" "x+y+z=9`
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