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

Options

A. `y-3z-6=0`
B. `y-3z+6-0`
C. `y-z-1=0`
D. `y-z+1=0`

Answer

B

Explanation

Equation of the planes passig through line of intersection of the planes x+y+z=1 and 2x+3y-z+4=0 is
`(x+y+z-1)+lamda(2x+3y-z+4)=0`
`rArr(1+2lamda)x+(1+3lamda)y+(1-lamda)z+(1-+4lamda)=0` . .. (i)
Since, Eq. (i) is parallel to X-axis, therefore
`(1+2lamda)=0rArrlamda=(-1)/(2)`
On substituting the value of `lamda` in Eq. (i), we get
`(0)x+(1-(3)/(2))y+(1+(1)/(2))z+(-1-2)=0`
`rArr" "-(1)/(2)y+(3)/(2)z-3=0`
`rArr" "y-3z+6=0`