Suppose we have:
$$\vec{a} = \begin{bmatrix} a_x \ a_y \end{bmatrix}$$
$$\vec{b} = \begin{bmatrix} b_x \ b_y \end{bmatrix}$$
I am wondering why $\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y$.
Let’s prove this by having a concrete example:
Suppose we have:
$$\vec{a} = \begin{bmatrix} a_x \ a_y \end{bmatrix}$$
$$\vec{b} = \begin{bmatrix} b_x \ b_y \end{bmatrix}$$
I am wondering why $\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y$.
Let’s prove this by having a concrete example: