BITSAT 2019 Paper

(c) Equation of the first line L‌1 is

x−1

2

=

y−2

3

=

z−3

4

and that of the second line L‌2 is

x−4

5

=

y−1

2

=

z−0

1

Clearly, these lines are not parallel (the ratios of D.R. are not equal).
Any point P on the first line is (1 + 2λ,, 2+3λ, 3 + 4λ) and any point Q on the second line is (4 + 5µ, 1 + 2µ, µ). If these two points P and Q are identical then.
1 + 2λ = 4 + 5µ ...(1)
2 + 3λ = 1 +2µ ...(2)
3 + 4λ = µ ...(3)
From (2) and (3), we get λ = µ = -1, which also satisfies (1). Thus the two lines L‌1 and L‌2 ; intersect and the coordinates of the point of intersection are (-1, -1 , -1).