- 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.

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** - (a
**u**+ b**v**)**·****w**= (a**u**)**·****w**+ (b**v**)**·****w**