VITEEE 2010 Paper

The given line is

→

r

=2

^

i

−2

^

j

+3

^

k

+λ(

^

i

−

^

j

+4

^

k

)
On comparing it with

→

r

=

→

a

+t

→

b

, we get

→

a

=2

^

i

−2

^

j

+3

^

k

,

→

b

=

^

i

−

^

j

+4

^

k

Also, the plane is

→

r

.(

^

i

+5

^

j

+

^

k

)=5
On comparing it with

→

r

.

→

n

=d , we get

→

n

=

^

i

+5

^

j

+

^

k

‌and‌d=5
Since,

→

b

.

→

n

=(

^

i

−

^

j

+4

^

k

).(

^

i

+5

^

j

+

^

k

)
=1−5+4=0
∴ Given line is parallel to the given plane.
Now, distance between the line and the plane is given by required distance..