Finding the area of a triangle made by two vectors is an exciting use of something called determinants!

1. Vectors: Let’s look at two vectors. We can write them as:

   • Vector u = (x₁, y₁)
   • Vector v = (x₂, y₂)

2. Area Calculation: To find the area A of the triangle created by these two vectors, we can use this formula:

   • A = 1/2 × |det(u, v)|

3. Determinants: The determinant of the matrix that these vectors make looks like this:

   • det(u, v) = x₁ × y₂ - x₂ × y₁

Using determinants in this way helps us quickly calculate areas with linear algebra. Isn’t that cool? 🎉