Find the area of

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) = (1, –3, 1) and (b₁, b₂, b₃) = (1, 1, 1)

Recall the magnitude of the vector is

Now, we find.

Thus, the area of the parallelogram is square units.