The preview activity presented us with a vector
and led us through the process of describing all the vectors orthogonal to
Notice that the set of scalar multiples of
describes a line
a 1-dimensional subspace of
We then described a second line consisting of all the vectors orthogonal to
Notice that every vector on this line is orthogonal to every vector on the line
We call this new line the
orthogonal complement of
and denote it by
The lines
and
are illustrated on the left of
Figure 6.2.2.
A typical example appears on the right of
Figure 6.2.2. Here we see a plane
a two-dimensional subspace of
and its orthogonal complement
which is a line in