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The equation of the plane through the in...

The equation of the plane through the intersection of the planes `x+y+z=1` and `2x+3y-z+4 = 0` and parallel to x-axis is

A

y-3z+6=0

B

3y-z+6=0

C

y+3z+6=0

D

3y-2z+6=0

Text Solution

Verified by Experts

The correct Answer is:
A
The equation of the plane through the intersection of given
`(x+y+z-1)+k(2x+3y-z+4)=0` . . (i)
`impliesx(1+2k)+y(1+3k)+z(1-k)-1(1-4k)=0`
`because` Plane is parallel to X-axis,
`x(1+2k)=0`
`impliesk=-(1)/(2)`
Put k=-1/2 in Eq. (i) we get the required equation of plane which is `2(x+y+z-1)-2x-3y+z-4=0`
`impliesy-3z+6=0`
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