2x – y + 3z + 4 = 0 = ax + y – z + 2 ... (1)

 equation of plane through (1) is (2x – y + 3z + 4) + λ (ax + y – z + 2) = 0

x(2 + a λ ) + y( λ – 1) + z(3 – λ ) + (4 + 2 λ ) = 0 .... (2)

x – 3y + z = 0 = x + 2y + 2 + 1 ... (3)

 equation of plane passing through (3) is

(x – 3y + z) + μ (x + 2y + z + 1) = 0 ⇒ x(1 + μ ) + y(2 μ – 3) + z( μ + 1) + μ = 0 .... (4)

if lines (1) and (3) are coplanar, then

Solving this we get λ = – 1, μ = 1 ∴ a = – 2

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