Given two vectors in three diemsions,
neither a multiple of the other, a vector
perpendicular to both vectors can be found from the cross product of
and
The three vectors will form a linearly independent set.
Example:
Then
is a linaerly independent set.
Reversing the order of the cross multiplication changes the sign, so that
but does not change the property of being perpendicular.
and
are both perpendicular to and