# 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.

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