Find the equation of the plane passing through the line of intersection of the planes and and parallel to x-axis.

The equation of any plane through the line of intersection of the planes and is given by -

.

So, the equation of any plane through the line of intersection of the given planes is

.

.

∴ . …(1)

Since this plane is parallel to x-axis.

So, the normal vector of the plane (1) will be perpendicular to x-axis.

Direction ratios of Normal (a_1, b_1, c₁)≡ [(1 - 2λ), (1 - 3λ), (1 +)]

Direction ratios of x–axis (a_2, b_2, c₂)≡ (1,0,0)

Since the two lines are perpendicular,

a₁a₂ + b₁b₂ + c₁c₂ = 0

(1 - 2λ) × 1 + (1 - 3λ) × 0 + (1 + λ) × 0 = 0

⇒ (1 - 2λ) = 0

∴ λ = 1/2

Putting the value of λ in (1), we get -

⇒

⇒

Hence, the equation of the required plane is