Answer
See the explanation 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 scalar product can defined as: $u \cdot v=u_xv_x+u_yv_y+u_zv_z$
The algebraic laws for the dot product are described as below:
a) The null vector $u \cdot 0=0$
b) The dot product of two vectors will be zero when both vectors are perpendicular to each other.
c) The dot product of two vectors obeys the distributive property $u\cdot (v+w)=u \cdot v +u \cdot w$
d) The dot product of two vectors obeys the commutative property $u\cdot v=v \cdot u$
