The two adjacent sides of a parallelogram are and . Find the unit vector parallel to its diagonal. Also, find its area.

Given: Two adjacent sides of a parallelogram are

Then the diagonal of parallelogram is given by the resultant of .

Let the diagonal is .

Then

Then

∴ unit vector parallel to its diagonal is

And area of parallelogram ABCD is

∴

Hence, area of parallelogram ABCD is .