Question

The equation of the plane through the intersection of the planes ax + by + cz + d = 0 andlx + my + nz + p = 0 and parallel to the line y=0, z=0

Options

• (bl − am) y + (cl − an) z + dl − ap = 0

•  (am − bl) x + (mc − bn) z + md − bp = 0

•  (na − cl) x + (bn − cm) y + nd − cp = 0

• None of these

   

Answer 1

The equation of the plane passing through the intersection of the planes
ax + by + cz + d = 0
and lx + my + nz + p = 0
will be (​ax + by + cz + d) + λ(​lx + my + nz + p) = 0

x(a + ​λl) + y(b + ​λm) + z(c + ​λn) + (d + ​λp)=0  .......(1)

Since the plane is parallel to the line y=0 and z=0
a + ​λl=0
λ \[\frac{- a}{l}\]

putting the value of ​λ in equation (1), we get

\[x(a + (\frac{- a}{l})l) + y(b + (\frac{- a}{l})m) + z(c + (\frac{- a}{l}) n) + d + (\frac{- a}{l})p = 0\]

\[y(bl - am) + z(cl - an) + dl - ap = 0\]

Hence, option (a)