orthogonal

Perpendicular — two vectors with dot product exactly 0.

Two vectors $\mathbf u,\mathbf v \in \mathbb R^n$ are orthogonal if $\mathbf u\cdot\mathbf v = 0$ , written $\mathbf u\perp\mathbf v$ . This is this course's technical word for "perpendicular": in $\mathbb R^2$ and $\mathbb R^3$ it really is the $90°$ geometric angle, since $\mathbf u\cdot\mathbf v = \lVert\mathbf u\rVert\lVert\mathbf v\rVert\cos\theta$ is zero exactly when $\cos\theta = 0$ — but the dot-product test keeps working in $\mathbb R^n$ for any $n$ , where there's no picture to check against. The zero vector is orthogonal to every vector, itself included.