TITLE: Finding a unit vector perpendicular to another vector
QUESTION [39 upvotes]: For example we have the vector $8i + 4j - 6k$, how can we find a unit vector perpendicular to this vector?

REPLY [4 votes]: I want to add an answer for only two dimensions since it's much more simple:
If our vector is $$v = ai + bj$$
We can easily calculate the normal of $v$, because the normal of a vector is perpendicular to it. $$n = -bi + aj$$
$n$ is now a perpendicular vector to the vector v, it just has to be normalized, which is explained in other answers already.
$$n \rightarrow \frac{n}{\lVert n \rVert}$$