Dot Product (Scalar Product)

Definition

$$ \vec{A} \cdot \vec{B} = AB \cos\theta $$

Component Form

$$ \vec{A} \cdot \vec{B} = A_x B_x + A_y B_y + A_z B_z $$

Physical Meaning

The dot product measures how much one vector lies in the direction of another.

Example: Work done by a force

$$ W = \vec{F} \cdot \vec{d} $$