AP EAPCET 19-Aug-2021 Shift 2 Paper

Given that line L1 is passing through (2

^

i

−

^

k

)
and parallel to (3

^

i

−

^

j

+2

^

k

)
Let a1=2

^

i

−

^

k

and b1=3

^

i

−

^

j

+2

^

k

equation line L1:r=a1+λb1 ...(i)
Also given line L2 is passing through (2

^

i

+

^

j

−3

^

k

)
and parallel to (

^

i

−2

^

j

+

^

k

)
Let‌a2=2

^

i

+

^

j

−3

^

k

and

^

b

2=

^

i

−2

^

j

+

^

k

Equation of line L2:r=a2+µb2 ...(ii)
∴ Shortest distance between L1 and L2
d=|

(b1×b2).(a2−a1)

|b1×b2|

| ...(iii)
Consider b1×b2=|

^ i	^ j	^ k
3	−1	2
1	−2	1

|=3

^

i

−

^

j

−5

^

k

|b1×b2|=√32+(−1)2+(−5)2=√35
and a2−a1=(2

^

i

+

^

j

−3

^

k

)−(2

^

i

−

^

k

)
=

^

j

−2

^

k

(b1×b2).(a2−a1)=(3

^

i

−

^

j

−5

^

k

).(

^

j

−2

^

k

)
=−1+10=9
Now from Eq. (iii)
d=|

9

√35

|
⇒d=−

9

√35