Answer:
Here is a list of cross product properties:
End of Chapter
right-hand rule
Right hand rule.
The orientation of
u
×
v
is in the "thumb" direction if your fingers curl from
u
to
v
.
cross product, as area of parallelogram
Magnitude of Cross product.
The magnitude of
u
×
v
is the area of the parallelogram defined by the two vectors.
cross product, anti-commutative
Anti-commutative
u
×
v
= -(
v
×
u
)
cross product, collinear vectors
Co-linear operands yield zero vector.
u
×
u
=
0
(k
u
)
×
u
=
0
.
cross product, with zero vector
Cross product with zero vector yields zero vector.
u
×
0
=
0
×
u
=
0
cross product, not associative
Not associative
In general: (
u
×
v
)
×
w
=/=
u
×
(
v
×
w
)
cross product, distributive property
Distributive over vector addition
u
×
(
v
+
w
) =  
u
×
v
+
u
×
w
cross product, between coordinate axes
Cross product between coordinate axes
i
×
j
=
k
j
×
k
=
i
k
×
i
=
j
The next chapter discusses rectangular matrices.