If the straight lines x = 1 + s , y = − 3 − λ s , z = 1 + λ s and x = 2 t , y = 1 + t , z = 2 − t with parameters s and t respectively, are co-planar then λ equals

Question

If the straight lines x = 1 + s , y = − 3 − λ s , z = 1 + λ s and x = 2 t ​ , y = 1 + t , z = 2 − t with parameters s and t respectively, are co-planar then λ equals

TestHub · Accepted Answer

Given lines 1 x − 1 ​ = − λ y + s ​ = λ z − 1 ​ = s and 1/2 x ​ = 1 y − 1 ​ = − 1 z − 2 ​ = t are coplanar then plan passing through these lines has normal perpendicular to these lines ⇒ a − bλ + c λ = 0 and 2 a ​ + b − c = 0 (where a , b , c are direction ratios of the normal to the plan) On solving, we get λ = − 2

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