KEAM 2010 Math Paper

The given line is
or ‌‌

→

r

=

→

a

+λ

→

b

where

→

a

=(2

∧

i

+2

∧

j

−

∧

k

)
and

→

b

=2

∧

i

+

∧

j

−2

∧

k

The equation of plane is

→

r

⋅(

∧

i

+2

∧

j

+2

∧

k

)=10
or

→

r

⋅

∧

n

=d
where

∧

n

=(

∧

i

+2

∧

j

+2

∧

k

)
since, =2+2−4=0
Therefore, the line is parallel to the plane.
Hence, the required distance
=|‌

2+4−2−10

√9

|
=|‌

−6

3

|=2