Correct option is A. (bl – am)y + (cl – an) z + dl – ap = 0
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
⇒ \(\lambda=-\cfrac{a}1\)
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
