Talk:Orthogonal

Orthogonality is a concept defined in mathematics for spaces in which a dot product or inner product is defined. Two entities in that space are orthogonal if their dot product is zero.

In common speech (in an Euclidean space) two lines are orthogonal if they form a right angle, i.e. if the angle between them is 90 degrees. This is equivalent to saying that the dot product of two non-zero vectors aligned with the lines is zero, which explains the more general definition given above. Similarly, a line is said to be orthogonal to a plane if the two form a right angle, and two planes are said to be orthogonal if they intersect in a right angle. The term perpendicular is also used to describe this relationship.

Two straight lines in an Cartesian coordinate system are orthogonal if the product of their slopes is -1.

Several vectors are called pairwise orthogonal if any two of them are orthogonal. Non-zero pairwise orthogonal vectors are always linearly independent.

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the above has been lost in the current revision -- I think some of it should be resotred to give the general concept -- Tarquin 12:08 Mar 11, 2003 (UTC)

should it better be moved to the perpendicular page? if you want to add it back, additional graphical representations are fine. -- Wshun