Using the Vector Cross product to find the Area of a Triangle

Let’s see how to use the Vector Cross product to find the Area of a Triangle. Here we will see that half of the magnitude of the cross product of vector AB and AC gives the area of the triangle ABC. (reference: the image below)

Using Cross product to find Area of a Triangle. Here we can see that half of the magnitude of the cross product of vector AB and AC gives the area of the triangle ABC.
Using Cross product to find Area of a Triangle

Let, AB and AC are 2 vectors and these are taken as 2 adjacent sides of triangle ABC. The magnitude of AB and AC are b and a respectively, which are the length of two sides of the triangle as well.

L is the height of the triangle and θ is the angle CAB.
Hence, L = a sin θ

Area of ABC = (½) AB . L = (½) b a sin θ ………… (1)
And, |AB x AC| = b a sin θ …………… (2)

So, Area of ABC = (½) |AB x AC|

Here we can see that half of the magnitude of the cross product of vector AB and AC gives the area of the triangle ABC.

Using the Vector Cross product to find the Area of a Triangle
Share about physicsteacher.in
Scroll to top