Using Vector Cross product to find Area of a Parallelogram

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

ABCD is a parallelogram and its area is twice the area of the ABC triangle.

As Area of ABC triangle = (½) | AB x AC |, (see the proof: here) hence we can represent the area of ABCD as per the following way:

Area of ABCD = 2 . Area of ABC = 2. (½) | AB x AC| = | AB x AC|

Here we can see that the magnitude of the cross product of vector AB and AC gives the area of the parallelogram ABCD.

Using Vector Cross product to find Area of a Parallelogram
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