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Question:

Two lines L1: x=5, y-3-α=z-6 and L2: x=α, y-1=z-2-α are coplanar. Then α can take value(s)

1

2

3

4

Solution:

x-5=y-3-α=z-6
x-α=y-1=z-2-α
will be coplanar, if the shortest distance is zero.
⇒∣∣∣∣5-α003-α6-012-α-α∣∣∣∣=0
⇒(5-α)(α²-α+4)=0, α=1,4,5
Hence, option A and D are correct.