3.2 Work

Dot Products

A dot product is a mathematical operation between two vectors that produces a scalar. It measures how much two vectors point in the same direction.

If ${\vec{A} = a_x \hat{i} + a_y \hat{j} + a_z \hat{k}}$ and ${\vec{B} = b_x \hat{i} + b_y \hat{j} + b_z \hat{k}}$, then: ${\vec{A} \cdot \vec{B} = a_x b_x + a_y b_y + a_z b_z}$

It can also be written as: ${\vec{A} \cdot \vec{B} = AB \cos \theta}$ where ${\theta}$ is the angle between the two vectors.