BITSAT 2015 Paper

The equations of given lines can be written as
L1 : x - 5 =

y

3−α

=

z

−2

L2 : x - α =

y

−1

=

z

2−α

Since, these lines are coplanar.
Therefore |

5−α	0−0	0−0
0	3−α	−2
0	−1	2−α

| = 0
⇒ (5 – α) (3 – α) (2 – α) – 2 = 0
⇒ (5 – α) (6 – 3α – 2α + α2 – 2] = 0
⇒ (5 – α) (α2 – 5α + 4] = 0
⇒ (5 – α) (α – 1)(α – 4) = 0
⇒ α = 1, 4, 5