General Math Term, if two objects are *orthogonal*, then they are $90\degree$ apart. ## Synonyms When two objects are - At right angles - Perpendicular - Orthogonal - [[Normal Vector|Normal]] ## Method of finding Orthogonal Vectors ### Switch & Flip **Only use when you only need a few orthogonal vectors, and don't care what those vectors are. This is a solution to get *some* angles** To find a vector orthogonal to some $\R^2$ vector $\vec v$, swap the $x$ and $y$ and make one negative. $\huge\begin{align*} \vec v &= \mat {3 \\ 4} \\ \mat{4 \\ 3} &\to \mat{-3 \\ 4} \\ \end{align*}$ This worlds in in higher dimensions only if all elements except 2 are 0. ### Plug in arbitrary variables $\huge\begin{align*} \vec v &= \mat{1 \\ 3} \\ \vec v \cdot \vec u &= 0 \\ \vec u _{x}+3\vec u_{y} &= 0 \\ \vec u _{y}&= 1 \\ \vec u _{x}+3 &= 0 \\ \vec u _{x} &= -3 \\ \vec u &= \mat{-3 \\ 1} \end{align*}$ Because this equation *describes a line*, any $x$ will map to some $y$. Similarly, in higher dimension you give, assign arbitrary values to *all elements but 1*, and solve for the remaining variable.