Yes, it can.
Note- For denoting vector quantities, I will bold the letters. The unbolded letters will be the magnitude, or scalar quantities, of the vectors.
Let's first define the scalar (or dot) product. The scalar product of two vectors can either defined as:
(2) For A= < a1,a2,a3 > and B=< b1,b2,v3 >, A
For the case of (1), the scalar product will never be negative due to the magnitudes of the vectors since the magnitude is always positive. However, the scalar product will be negative when
An example of a negative scalar product for the case of (2) would be if you had vector A= <2,4,-5> and B=<-1,2,3>.