What is the dot product of two planar vectors $\vec{u} = (x_1, y_1)$ and $\vec{v} = (x_2, y_2)$, and what does $\vec{u} \cdot \vec{v} = 0$ imply for non-zero vectors?

Question

Accepted Answer

$\vec{u} \cdot \vec{v} = x_1 x_2 + y_1 y_2 = |\vec{u}||\vec{v}|\cos	heta$; $\vec{u} \cdot \vec{v} = 0$ indicates that the vectors are orthogonal (perpendicular).

What is the dot product of two planar vectors $\vec{u} = (x_1, y_1)$ and $\vec{v} = (x_2, y_2)$, and what does $\vec{u} \cdot \vec{v} = 0$ imply for non-zero vectors?

Answer

Explanation