AIEEE 2004 Math Solved Paper

Let a point on the line
x=y+a=z‌ is ‌(λ,λ−a,λ)
and a point on the line
x+a=2y=2z‌ is ‌(µ−a,‌

µ

2

,‌

µ

2

),
then direction ratio of the line joining these points are
λ−µ+a,λ−a−‌

µ

2

,λ−‌

µ

2

If it represents the required line, then
‌

λ−µ+a

2

‌=‌

λ−a− µ 2

1

‌=‌

λ− µ 2

2

on solving we get λ=3a,µ=2a
∴ The required points of intersection are
(3a,3a−a,3a)‌ and ‌(2a−a,‌

2a

2

,‌

2a

2

)
or (3a,2a,3a) and (a,a,a)