If and are unit vectors forming an angle of 30^o, find the area of the parallelogram having and as its diagonals.

Given two unit vectors and forming an angle of 30°.

We know the cross product of two vectors and forming an angle θ is

where is a unit vector perpendicular to and .

Given two diagonals of parallelogram and

Recall the area of the parallelogram whose diagonals are given by the two vectors and is.

We have

We have

But, we found .

is a unit vector

Thus, area of the parallelogram is square units.