So, we are currently studying algebraic vectors in my math class, and I noticed an interesting property I couldn't explain that my teacher didn't want to explain since it has to do with material outside the corriculum, and didn't want to confuse students.
What I found was that the area of a triangle ABC define by the vectors AB and AC is equal to a half of the magnitude of the cross product of AB and AC (0.5 * |AC| * |AB| * sin(θ) with θ being the angle between AB and AC).
Is this coincidental or is there some relation between the area of the triangle and the cross product?
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$\begingroup$That is not a coincidence. The magnitude of the cross product of two vectors equals the area of the parallelogram spanned by these two vectors. And since a triangle is half of a parallelogram, your relation follows.
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