and 
.
.
.
.
.
.
.
and 
are the vectors from the previous
exercise, explain why it is true that
Note - just computing both sides of the equation and comparing is not a sufficient explanation. Your explanation must include references to properties of the cross product.
perpendicular to 
such that
where 
and 
.
is not equal to 
. Remember
that just showing that the results are not the same for specific fixed
vectors is not
enough. Instead, you should do the calculations with arbitrary
three-dimensional vectors.
is perpendicular to
and perpendicular to 
, where 
and 
are arbitrary three-dimensional vectors.
where 
and 
are arbitrary three-dimensional vectors, and
then explain how this identity implies the equation
where 
is the angle between 
and 
.