If ¯a and ¯b are two vectors as shown in the figure, then ¯a.¯b will equal to |¯a||¯b| cos θ
We know that for two vectors ¯a and ¯b, the dot product ¯a.¯b is defined as |¯a||¯b| cos θ , where θ is the angle between the two vectors. This θ is the angle between two line segments representing the vectors when their initial points are same. In the given figure, the initial point of ¯b is joined to terminal point of ¯a.
So the required angle would be (π−θ) as shown.
So ¯a.¯b=|¯a||¯b| cos(π−θ)
=−|¯a||¯b| cos θ