Orthogonality

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle. In 2- or 3-dimensional Euclidean space, two vectors are orthogonal if their dot product is zero, i.e. they make an angle of 90° or /2 radians. Hence orthogonality of vectors is a generalization of the concept of perpendicular. In terms of Euclidean subspaces, the orthogonal complement of a line is the plane perpendicular to it, and vice versa. Note however that there is no correspondence with regards to perpendicular planes, because vectors in subspaces start from the origin.

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High Quality Content by WIKIPEDIA articles! In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle. In 2- or 3-dimensional Euclidean space, two vectors are orthogonal if their dot product is zero, i.e. they make an angle of 90° or p/2 radians. Hence orthogonality of vectors is a generalization of the concept of perpendicular. In terms of Euclidean subspaces, the orthogonal complement of a line is the plane perpendicular to it, and vice versa. Note however that there is no correspondence with regards to perpendicular planes, because vectors in subspaces start from the origin.