Find the area of the parallelogram whose diagonals are : and

Question

Philoid · Accepted Answer

Given two diagonals of a parallelogram are and

Let and

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

Here, we have (a₁, a₂, a₃) = (4, –1, –3) and (b₁, b₂, b₃) = (–2, 1, –2)

Recall the magnitude of the vector is

Now, we find.

Thus, the area of the parallelogram is 7.5 square units.