Find the area of the parallelogram determined by the vectors :

and

Given two vectors and are sides of a parallelogram

Let and

Recall the area of the parallelogram whose adjacent sides are given by the two vectors and is where

Here, we have (a₁, a₂, a₃) = (2, 1, 3) and (b₁, b₂, b₃) = (1, –1, 0)

Recall the magnitude of the vector is

Now, we find.

Thus, area of the parallelogram is square units.