COMEDK Exam 2022 Solved Paper

Given lines are

x−1

1

=

y−1

2

=

z−2

3

=λ (let)
⇒ x=λ+1,y=2λ+1,z=3λ+2
and

x−5

2

=

y−2

1

=z=µ (let)
⇒ x=2µ+5,y=µ+2,z=µ
For point of intersection, we have
λ+1=2µ+5‌and‌2‌λ+1=µ+2‌and‌3‌λ+2=µ
λ−2µ=4..........(i)
2λ−µ=1 ..........(ii)
3λ−µ=−2 ..........(iii)
On solving Eqs. (ii) and (iii), we get

2λ	−µ	=1
3λ	−µ	=−2
−	+	+
−λ	=	3
λ	=	−3

So, µ=-7
Now, put λ=−3 and µ=−7 in Eq. (i), we get
−3+14=11≠4
Hence, the lines do not intersect.
Hence, option (d) is correct.