L.H.S. =
= R.H.S.
Hence, proved.
If diagonals of a parallelogram are then find the area of the parallelogram.
Let the sides of the parallelogram be whose diagonals are
The unit vector perpendicular to vectors is given by,
We have,
and
Therefore,
and
∴ , is the required unit vector.
What is the angle between
Vector is perpendicular to the plane containing
is the resultant of
therefore lies in the plane containing
∴ Angle between and is
Alternatively: