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mkkrnfoo85
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"The area of a parallelogram spanned by two vectors, v1 and v2, is ||v1 X v2||."
Would someone help me understand why this is true?
Would someone help me understand why this is true?
A cross product is a mathematical operation that takes two vectors as inputs and produces a third vector that is perpendicular to both of the input vectors.
The magnitude of the cross product of two vectors is equal to the area of the parallelogram formed by those two vectors. This means that the cross product can be used to calculate the area of a 2D shape.
The formula for calculating the cross product of two 3D vectors (a and b) is: a x b = (a_{y}b_{z} - a_{z}b_{y})i + (a_{z}b_{x} - a_{x}b_{z})j + (a_{x}b_{y} - a_{y}b_{x})k
The cross product can only be used to calculate the area of 2D shapes. It cannot be used for 3D shapes.
The direction of the cross product is determined by the right-hand rule. This means that if you curl the fingers of your right hand from vector a to vector b, your thumb will point in the direction of the resulting cross product vector.