KEAM 2016 Math Paper

Given equation of straight lines are
or ‌‌‌

x−3

−1

=‌

y+4

2

=‌

z−5

2

=λ......(i)
and ‌

3−x

−1

=‌

y+4

2

=‌

z−5

7

=µ
or, ‌

x−3

1

=‌

y+4

2

=‌

z−5

7

=µ.....(ii)
From Eq. (i) , coordinates are
(−λ+3−2λ−4,2λ+5)
From Eq. (ii) coordinates are
(µ+3,2µ−4,7µ+5)
For intersecting the given lines,
−λ+3=µ+3
⇒‌‌µ+λ=0.....(iii)
−2λ−4=2µ−4
⇒‌‌2µ+2λ=0 ....(iv)
2λ+5=7µ+5
⇒‌‌7µ−2λ=0....(v)
From Eqs. (iii), (vi), (v)
µ=0,λ=0
Hence, intersecting points are