dot product

Multiply matching components and add — turns two vectors into one number measuring how aligned they are.

The dot product of $\mathbf{u}=\langle u_1,u_2\rangle$ and $\mathbf{v}=\langle v_1,v_2\rangle$ is $\mathbf{u}\cdot\mathbf{v} = u_1v_1+u_2v_2$ , a single scalar rather than a vector. Equivalently, $\mathbf{u}\cdot\mathbf{v} = |\mathbf{u}||\mathbf{v}|\cos\theta$ for the angle $\theta$ between them, which makes the dot product zero exactly when two nonzero vectors are orthogonal (perpendicular).

Examples

$\langle 4,-6\rangle \cdot \langle 9,6\rangle = 36-36=0$ , so those two vectors are orthogonal.