In elementary geometry, orthogonal is the same as perpendicular. Two lines or curves are orthogonal if they are perpendicular at their point of intersection.
Two vectors 
and 
of the real plane 
or the real space 
are orthogonal iff their dot product 
. This condition has been exploited
to define orthogonality in the more abstract context of the 
-dimensional real space 
.
More generally, two elements 
and 
of an inner product space 
are called orthogonal if the inner
product of 
and 
is 0. Two subspaces 
and 
of 
are called orthogonal if every element of 
is orthogonal to every element of 
. The same definitions can be applied to any symmetric
or differential k-form and to any Hermitian form.
