A good answer might be:

Will v · v ever be negative?
No, since length is always zero or positive.
Will v · v ever be zero?
Yes, when v is the zero vector.

Properties of Dot Product

Another property of the dot product is:

(au + bv) · w = (au) · w + (bv) · w, where a and b are scalars

Here is the list of properties of the dot product:

u · v = |u||v| cos θ
u · v = v · u
u · v = 0 when u and v are orthogonal.
0 · 0 = 0
|v|² = v · v
a (u·v) = (a u) · v
(au + bv) · w = (au) · w + (bv) · w

QUESTION 7:

(Trick Question: ) What is u · v · w ?