Cross products

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Cross Product:

• In 2 Dimension the area of a parallelogram formed by 2 vectors is the cross product of the 2 vectors
• $\hat{i}\times \hat{j}$ = +1 and $\hat{j}\times \hat{i}$ = -1
• The order of the vectors matters. if the second vector is to the left of first then the value is positive, else negative.

Reminder

Transclude of The-determinant#^75e0d5

• The cross product of 2 vectors is the determinant of the matrix, formed using the 2 vectors, where the first column is the co-ordinates of the first vector, and the second column the co-ordinates of the second vector.
• Because the matrix transformation denotes, where the unit vectors land after a transformation, and their determinant is the areas of the unit vectors, which is the same as the area between the given vectors.
• The cross product of 2 vectors, that are perpendicular will be maximum, than 2 vectors of the same magnitude but with different order between them
• The cross product is a vector and not a number, the above mentioned … gives us a way to measure the magnitude of the cross product.
• The direction of the vector is $\perp$ to the parallelogram formed by the 2 vectors. Even then there are 2 directions $\perp$ to the parallelogram, the direction is decided by the right hand rule