Area of a Parallelogram via the Cross Product:
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Find the area of the parallelogram defined by the four points shown.
The area is equal to the magnitude of the cross product of vectors representing two adjacent sides:
Area = |AB ´
AD|
First we find the vectors:
AB = [2 - (-1)]i + [-1 - 2]j = 3i - 3j
AD = [3 - (-1)]i + [4 - 2]j = 4i + 2j
Area = |AB ´
AD| = 18.
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