If are three vectors, find the area of the parallelogram having diagonals and

Question

Philoid · Accepted Answer

Given, and

We need to find area of the parallelogram with vectors and as diagonals.

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

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

Recall the magnitude of the vector is

Now, we find.

Thus, area of the parallelogram is square units.