Two lines L_1 : x = 5, y 3 - = z -2 and L_2 : x = , y -1 = z 2 - are coplanar. Then α can take value(s)

JEE Advanced 2013 Mathematics question

Two lines and are coplanar. Then α can take value(s)

(A)1Correct
(B)2
(C)3
(D)4Correct

Answer: (A),(D)

Solution

passes through (5, 0, 0) with direction (0, 3 − α, −2) and through (α, 0, 0) with direction (0, −1, 2 − α). Coplanarity: $ α - 5 & 0 & 0 0 & 3 - α & -2 0 & -1 & 2 - α

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Question ID VK-026230