Dot Product of Two Vectors
In 3-space, the dot product of two vectors is a scalar. The dot product of vectors and
is
(1)
There is also an alternative form of
(2)
where

Cross Product of Two Vectors
In 3-space, the cross product of two vectors is a vector. The cross product of vectors and
is
(3)
There is also an alternative form of
(4)
where

Orthogonal Vectors
Two non-zero vectors and
are orthogonal, if and only if,
.
Parallel Vectors
Two non-zero vectors and
are parallel, if and only if,
.