dot product

The dot product or scalar product of $\vec{u}$ and $\vec{v}$ is $\vec{u}\cdot \vec{v}$. The resulting value is a scalar. The dot product is 0 when the vectors are orthogonal to each other.

$\vec{A}\cdot \vec{B}=AB\cos \varphi =|\vec{A}||\vec{B}|\cos \varphi$

• length of A (or B) times the length of A (or B) in the direction of B (or A), a.k.a the length of the other side of the triangle
• $\varphi$ is the acute or flat angle between $\vec{A}$ and $\vec{B}$

The dot product is equal to the sum of the product of the corresponding components. For example, if they are two dimensional, then: $\vec{u}\cdot \vec{v}=u_x\cdot v_x+u_y\cdot v_y$

# assume u, v are two tuples of arbitrary dimensions
assert len(u) == len(v)
u_dot_v = sum([u_i * v_i for u_i, v_i in zip(u, v)])