Answer :

The equation of the plane through the intersection of


the planes ax + by + cz + d=0 and lx + my + nz + p=0 is given as,


(ax + by + cz + d) + λ(lx + my + nz + p)=0


[where λ is a scalar]


x(a + lλ) + y(b + mλ) + z(c + nλ) + d + pλ=0


Given, that the required plane is parallel to the line y=0, z=0 i.e. x - axis so, we should have,


1(a + lλ) + 0(b + mλ) + 0(c + nλ)=0


a + lλ=0



Substituting the value of λ we get,



(alx + bly + clz + dl) - a(lx + my + nz + p)=0


alx + bly + clz + dl - alx + amy + anz + ap=0


bly + clz + dl - amy - anz - ap=0


(bl - an)y + (cl - an)z + dl - ap=0


Therefore, the equation of the required plane is


(bl–am)y + (cl–an)z + dl–ap=0

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