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Area is the measure of the size of a surface or a region. It is typically measured in square units, such as square meters or square inches.
The area of a rectangle can be calculated by multiplying its length by its width. This can be written as A = l * w, where A is the area, l is the length, and w is the width.
The cross product of two vectors is a vector that is perpendicular to both of the original vectors. Its magnitude is equal to the product of the magnitudes of the original vectors multiplied by the sine of the angle between them.
The cross product of two vectors, u and v, can be calculated using the following formula: u x v = (u2v3 - u3v2, u3v1 - u1v3, u1v2 - u2v1). This results in a vector perpendicular to both u and v.
The magnitude of the cross product of two vectors, u and v, is equal to the area of the parallelogram formed by those two vectors. This can be written as ||u x v|| = ||u|| * ||v|| * sin(θ), where θ is the angle between the two vectors.