If the straight lines x - 1 2 = y + 1 k = z 2 and x + 1 5 = y + 1 2 = z k are coplanar, then the plane(s) containing these two lines is(are)

JEE Advanced 2012 Mathematics question

If the straight lines and are coplanar, then the plane(s) containing these two lines is(are)

(A)y + 2z = −1
(B)y + z = −1Correct
(C)y − z = −1Correct
(D)y − 2z = −1

Answer: (B),(C)

Solution

The lines pass through A(1, −1, 0) and B(−1, −1, 0) with directions (2, k, 2) and (5, 2, k). Coplanarity: . For k = 2: normal $(2, 2, 2)×(5, 2, 2) = (0, 6,

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Question ID VK-026120