The cross product of
p and
q
returns a new vector orthogonal to both
p and
q.
Note
that the cross product is a vector.
The
cross-product obeys the
right
hand rule-
Using
your right hand, point your fingers in the direction of p
- Now
curl your fingers towards q
- Your
thumb will point in the direction of the cross-product
A
positive rotation about the
p x
q axis
will rotate
p
towards
q.Example:
Intuitively, the
normal should be along the z-axis because the triangle lies in
the xy
plane.
Cross product - geometric interpretation
The
magnitude of the cross product is the area of the parallelogram spanned by the
two vectors.
This
gives a really easy way to compute a triangle’s area, using vectors along the
triangle’s edges:
A
triangle’s perimeter is the sum of its edge lengths.