If I have a vector $\vec{v}$, is there a standard concise notation for the unit vector in the same direction of $\vec{v}$ that is $\frac{\vec{v}}{|\vec{v}|}$?

  • $\begingroup$ I don't think so... $\endgroup$
    – copper.hat
    May 21, 2015 at 15:15
  • $\begingroup$ You can simply define one. But, to me, there seems no need to have one such. $\endgroup$
    – Yes
    May 21, 2015 at 15:18

1 Answer 1


Sometimes the notation $$\hat v = \frac{v}{\|v\|_2}$$ is used. I've especially seen it on wikipedia and 3D-Graphics related articles containing math.

  • $\begingroup$ Indeed, if I see any notation to signify a vector has unit length (or a normalized vector), it's \hat. Not to say it's standard, but it's the only one I can ever recall seeing. $\endgroup$
    – pjs36
    May 21, 2015 at 15:23
  • $\begingroup$ Why is there a subscript 2 in the denominator? $\endgroup$
    – nosyarg
    May 21, 2015 at 16:08
  • $\begingroup$ @nosyarg To clarify that we are talking about the euclidean norm. $\endgroup$
    – AlexR
    May 21, 2015 at 16:09
  • $\begingroup$ Ok so it means the same thing as$\frac{\vec{v}}{|\vec{v}|}$? $\endgroup$
    – nosyarg
    May 21, 2015 at 16:11
  • $\begingroup$ @nosyarg Yes, it's just cleaner. $\endgroup$
    – AlexR
    May 21, 2015 at 16:12

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