If the lines 2 x − 1 = 3 y + 1 = 4 z − 1 and 1 x − 3 = 2 y − k = 1 z intersect, then k is equal to

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If the lines 2 x − 1 ​ = 3 y + 1 ​ = 4 z − 1 ​ and 1 x − 3 ​ = 2 y − k ​ = 1 z ​ intersect, then k is equal to

TestHub · Accepted Answer

Any point on 2 x − 1 ​ = 3 y + 1 ​ = 4 z − 1 ​ = t is ( 2 t + 1 , 3 t − 1 , 4 t + 1 ) And any point on 1 x − 3 ​ = 2 y − k ​ = 1 z ​ = s is ( s + 3 , 2 s + k , s ) Given lines are intersecting ⇒ t = − 2 3 ​ and s = − 5 ∴ k = 2 9 ​

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