The Cross Product
The cross product of two vectors,
c
=
a × b
has the following properties:
Magnitude:
c = a b sin θ
The direction of
c
is
perpendicular
to the plane spanned by
a
and
b
and is determined by the
right-hand rule.
Non-commutative:
a × b
= -
b × a
Algebraic formula:
c
=
a × b
= (a
y
b
z
- b
y
a
z
)
+ (a
z
b
x
- b
z
a
x
)
+ (a
x
b
y
- b
x
a
y
)
+
(az bx - bz ax ) 
+ (ax by - bx
ay ) 
+
(az bx - bz ax ) + (ax by - bx
ay )