Lec 1: Dot Product

Dot product: $\vec{A} \cdot \vec{B} = \sum_{i=1}^n A_iB_i$

Geometrically: $\vec{A} \cdot \vec{B} = |\vec{A}| \cdot |\vec{B}| cos\theta$

We can use the dot product and the length to find the angle between any vectors

Sign of $\vec{A}\cdot\vec{B}:$

>0 if angle less than 90 degrees, pointing at the same direction

=0 if angle is 90 degrees, perpendicular

<0 if angle is greater than 90 degrees, pointing at the opposite direction