Two lines L 1 : x = 5 , 3 − α y = − 2 z L 2 : x = α , − 1 y = 2 − α z are coplanar. Then, α can take value (s)

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Two lines L 1 ​ : x = 5 , 3 − α y ​ = − 2 z ​ L 2 ​ : x = α , − 1 y ​ = 2 − α z ​ are coplanar. Then, α can take value (s)

TestHub · Accepted Answer

The equations of given lines can be written as L 1 ​ : x − 5 = 3 − α y ​ = − 2 z ​ L 2 ​ : x − α = − 1 y ​ = 2 − α z ​ ​ Since, these lines are coplanar. Therefore, ​ 5 − α 0 0 ​ 0 − 0 3 − α − 1 ​ 0 − 0 − 2 2 − α ​ ​ = 0 ⇒ ( 5 − α ) ( 3 − α ) ( 2 − α ) − 2 = 0 ⇒ ( 5 − α ) ( 6 − 3 α − 2 α + α 2 − 2 ] = 0 ⇒ ( 5 − α ) ( α 2 − 5 α + 4 ] = 0 ⇒ ( 5 − α ) ( α − 1 ) ( α − 4 ) = 0 ⇒ α = 1 , 4 , 5 ​

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