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The equation of the plane passing throug...

The equation of the plane passing through the intersection of `x + 2y + 3x + 4 = 0 and 4x + 3y + 2z+ 1 = 0` and the origin `(0.0, 0)` is

A

`3x+2y+z+1=0`

B

`3x+2y+z=0`

C

`2x+3y+z=0`

D

`x+y+z=0`

Text Solution

Verified by Experts

The correct Answer is:
B
Equation of plane passing through the intersection of given planes is
`(x+2y+3z+4)+lamda(4x+3y+2z)+1)=0` . . .(i)
Plane (i) Passing through the origin i.e. (0,0,0)
`:." "4+lamda=0rArrlamda=-4`
On putting the value of `lamda` in Eq. (i) we get
`(x+2y+3y+4)-4(4x+3y+2z+1)=0`
`rArr-15x-10y-5z=0rArr3x+2y+z=0`
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