Answer
See below.
Work Step by Step
The two vectors in component form can be expressed as:
$u =\lt u_{1}, u_{2}, u_{3}\gt $ and $v =\lt v_{1}, v_{2}, v_{3}\gt $
Their vector cross product can defined as:
$u \times v=|u||v| \sin \theta$
The algebraic laws for the dot product are described as below:
a) The null vector $0 \times u=0$
b) $u\times (v \times w)=(u \cdot w) v -( u \cdot v) w$
c) The cross product of two vectors obeys the distributive property $u\times (v+w)=u \times v +u \times w$
d) The dot product of two vectors does not obey the commutative property, that is, $v \times u =-( u \times v)$
