The two adjacent sides of a parallelogram are represented by vectors 2

^

i

−4

^

j

+ 5

^

k

and

^

i

−2

^

j

−3

^

k

. Find the unit vector parallel to one of its diagonals. Also, find the area of the parallelogram.
OR
If

→

a

=2

^

i

+2

^

j

+3

^

k

,

→

b

=−

^

i

+2

^

j

+

^

k

and

→

c

=3

^

i

+

^

j

are such that the vector (

→

a

+λ

→

b

) is perpendicular to vector

→

c

, then find the value of λ.