Manipal Entrance Test 2015 Math Paper

The lines are parallel to the vectors b1=

^

i

+2

^

j

−

^

k

and b2=−

^

i

+

^

j

−2

^

k

∴ The plane normal to the vector n is
b1×b2=|

^ i	^ j	^ k
1	2	−1
−1	1	−2

| =−3

^

i

+3

^

j

+3

^

k

The required plane passes through (

^

i

+

^

j

) and is normal to the vector n.
∴ Its equation is
r.n=a.n
⇒ r.(−3

^

i

+3

^

j

+3

^

k

) =(

^

i

+

^

j

).(−3

^

i

+3

^

j

+3

^

k

)
⇒ r.(−3

^

i

+3

^

j

+3

^

k

)=−3+3
⇒ r.(−

^

i

+

^

j

+

^

k

)=0