Let the two lines whose equations are L 1 : 2 x − 3 = 3 y − 2 = λ z − 1 and L 2 : 3 x − 2 = 2 y − 3 = 3 z − 2 lie in the same plane. If L 1 intersects a plane x + y + z = 15 at P , t

Question

Let the two lines whose equations are L 1 ​ : 2 x − 3 ​ = 3 y − 2 ​ = λ z − 1 ​ and L 2 ​ : 3 x − 2 ​ = 2 y − 3 ​ = 3 z − 2 ​ lie in the same plane. If L 1 ​ intersects a plane x + y + z = 15 at P , then distance of P from ( 3 , 4 , 3 ) is-

TestHub · Accepted Answer

Lines L 1 ​ & L 2 ​ are coplanar if ​ 3 − 2 ​ 2 − 3 ​ 1 − 22 ​ 3 ​ λ 3 ​ 2 ​ 3 ​ ​ = 0 ⇒ λ = 4 Let L 1 ​ : 2 x − 3 ​ = 3 y − 2 ​ = 4 z − 1 ​ = t ∴ Any point on it is P ( 2 t + 3 , 3 t + 2 , 4 t + 1 ) It lies on the plane x + y + z = 15 ⇒ 9 t + 6 = 15 or t = 1 ∴ Distance of P ( 5 , 5 , 5 ) from ( 3 , 4 , 3 ) = 3

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